Friedman R., Morgan J.W. — Smooth four-manifolds and complex surfaces :: Электронная библиотека попечительского совета мехмата МГУ

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Friedman R., Morgan J.W. — Smooth four-manifolds and complex surfaces

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Название: Smooth four-manifolds and complex surfaces

Авторы: Friedman R., Morgan J.W.

Аннотация:

This book applies the recent techniques of gauge theory to study the smooth classification of compact complex surfaces. The study is divided into four main areas: Classical complex surface theory, gauge theory and Donaldson invariants, deformations of holomorphic vector bundles, and explicit calculations for elliptic sur§ faces. The book represents a marriage of the techniques of algebraic geometry and 4-manifold topology and gives a detailed exposition of some of the main themes in this very active area of current research.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 528

Добавлена в каталог: 05.02.2014

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Предметный указатель

#, connected sum of manifolds      12
$#_{f}$ , fiber connected sum of $C^{\infty}$ elliptic surfaces      161
$A(Q,\epsilon)$ , the set of points a which satisfy $\int_{S^{4}}|x|^{2}d\mu_{a}\leq \epsilon$       250
$Aut^{\Sigma} B$ , the automorphisms of the elliptic surface B preserving the section $\Sigma$       76
$A_{0}(M)$ , automorphisms of the quadratic form of M which are the identity on all classes coming from the boundary      185
$b^{+}_{2}(M)$ , dimension of a maximal positive definite subspace of $H_{2}(M; \mathds{R})$       12
$b^{-}_{2}(M)$ , dimension of a maximal negative definite subspace of $H_{2}(M; \mathds{R})$       12
$B_{g.b.}(g,d)$ , the set of all surfaces S in B(g,d) such that $(S, j_{S})$ has generic branching behavior      64
$B_{n.c.j.}(g,d)$ , the set of isomorphism classes of elliptic surfaces in B(g,d) with nonconstant j-invariant      63
$B_{nod.}(g,d)$ , the set of all surfaces S in B(g,d) such that S is nodal      64
$B_{\Sigma}$ , $\bigcup_{\Sigma^{'}<\Sigma} Z(K_{\Sigma^{'}},\epsilon_{\Sigma^{'}})$       261
$C_{±}(V)$ , elements of even or odd degree in C(V)      375
$d(fr \Sigma)$ , the largest dimension of a stratum $\Sigma^{'}$ with $\Sigma^{'} < \Sigma$       261
$deg_{x} \varphi$ , local degree at x of the map $\varphi$ whose differential at x is Fredholm of index zero      350 351
$Det(\lambda)$ , determinant line bundle associated to $E^{+}(A)$       238
$det_{AS}(D)$ , the Atiyah — Singer determinant line bundle      385
$det_{BGS}(\mathcal{D})$ , the Bismut — Gillet — Soule determinant line bundle      391
$Diff^{+} M$ , group of orientation-preserving self-diffeomorphisms of M      12
$D^{0}_{T}$ , the pullback of $Div({\not{\partial}}_{T})$ to $\widehat{\mathcal{X}}^{0}(P)$       235
$D_{0}(M)$ , the subgroup of D(M) induced by compactly supported orientation-preserving self-diffeomorphisms      185
$D_{T}$ , the image of $D^{0}_{T}$ in $\mathcal{X}^{0}(P)$       235
$E^{+}(A)$ , the Atiyah — Hitchin — Singer deformation complex for the ASD connection A      237
$Fr(\widetilde{\Sigma})^{0}$ , the restriction of the fiber product over $\mathcal{M}{P^{'}, g)\times(M \times ... \times M - \Delta)$       258
$F_{0}$ , union of the strata of $X_{\delta}(P, g)$ whose points have trivial background connections      263
$F_{A}$ , the curvature of the connection A      232
$F_{A}^{+}$ , the self-dual part of $F_{A}$       255
$G(n_{1},... ,n_{t})$ , the semi-direct product $(\prod_{i=1}^{t}SO(4)) \times ((\prod_{i=1}^{t}SU(2))/\{\pm1\}) \rtimes \mathfrak{G}(n_{1},...,n_{t})$       252
$G_{k}$ , the elements in $SO(V; \mathds{C})$ fixing $k \in V$       397
$G_{S}$ , the homological invariant of the elliptic surface S      43
$III^{an}(B)$ , the set of all elliptic surfaces without multiple fibers whose Jacobian surface is B      75
$I_{0}^{*}$ , a Kodaira fiber      60
$I_{n}$ , a Kodaira fiber which is a cycle of n rational curves      51 52
$j_{S}$ , the j-function of the elliptic surface S      43
$K_{X}$ , the canonical bundle of the manifold X      11
$M^{conj}$ , the conjugate complex manifold corresponding to M      206
$M^{sch}$ , scheme version of $M_{c, S, L}$       337
$M_{0}$ , $\overline{M}_{0}$ , deformation functors for stable or semistable bundles on C with trivial determinant      357
$M_{0}^{0}$ , $\overline{M}_{0}^{0}$ , rigidified versions of $M_{0}$ , $\overline{M}_{0}$       363
$M_{c, S, L}$ , global moduli functor of L-stable bundles on S with $c_{1} = 0$ and $c_{2} = c$       334
$M_{c, S, L}^{0}$ , based version of $M_{c, S, L}$       336
$M_{M, V}$ , global moduli functor of holomorphic structures on V      303
$M_{V}$ , local moduli functor of germs of deformations of V      304
$m_{W}$ , multiplicity of the irreducible component W in the complex space Z      349
$Pic^{d} C$ , the set of isomorphism classes of line bundles on C of degree d      11
$P_{+}$ , projection onto the space of self-dual 2-forms      242
$P_{c}$ , the SU(2)-bundle over M with $c_{2} = c$       226
$p_{g}(S)$ , the geometric genus of S      18
$P_{n}(S)$ , the $n^{th}$ plurigenus of S      18
$q_{M}$ , intersection form of the oriented 4-manifold M      12
$r_{T}$ , restriction of connections to the 2-manifold T      234
$r_{T}^{0}$ , restriction of connections for the quotient space of connections modulo the based gauge group      234
$r_{\delta}$ , reflection about $\delta$       185
$S^{l}(M)$ , the $l^{th}$ symmetric product of M      244
$S_{min}$ , the minimal model of the complex surface S      21
$T(S, \{t_{i}\}, \{\xi_{i}\})$ , set of elliptic surfaces locally isomorphic to S except over the $t_{i}$ and with the same basic elliptic surface      102
$V_{\delta}(P,g)$ , thickened moduli space      247 257
$V_{\delta}(P,\lambda)$ , parametrized version of $V_{\delta}(P,g)$       260
$W_{\delta,p}(P, g)$ , subset of $V_{\delta}(P,g)$ whose measures do not have singular support at p      257
$W_{\delta,p}^{0}(P, g)$ , based version of $W_{\delta,p}(P, g)$       257
$W_{\lambda}(P, g_{M})$ , generalized connections with small curvature in a ball $B_{\lambda}$       434
$W_{\lambda}^{0}(P, g_{M})$ , based version of $W_{\lambda}(P, g_{M})$       435
$X(P,\lambda)$ , parametrized version of X(P,g)      245
$X_{\delta}(P,g)$ , thickened completion of the moduli space      260
$Y(P, \lambda)$ , $Y^{0}(P, \lambda)$ , parametrized versions of Y(P, g) and $Y^{0}(P, g)$       246
$Y^{0}(P, g)$ , a based version of Y(P, g)      246
$Y_{\delta}(P,N,g)$ , set of points of $X_{\delta}(P,g)$ whose associated measures do not have support on N      263
$Y_{\delta}^{0}(P,N,g)$ , based version of $Y_{\delta}(P,N,g)$       263
$Z(Q, \epsilon)$ , the intersection of $A(Q,\epsilon)$ with the set of those points $a \in X(Q,g_{0})$ whose center of mass is the north pole      250
$Z(\Sigma,\epsilon)$ , $Fr(\widetilde{\Sigma})^{0} \times_{G(n_{1},...,n_{t})} Z^{0}((n_{1}, ... , n_{t}), \epsilon)$       253
$Z^{0}((n_{1},...,n_{t}),\epsilon)$ , $\prod_{i=1}^{t}Z^{0}(Q_{n_{i}},\epsilon)$       253
$Z^{0}(Q, \epsilon)$ , based version of $Z(Q, \epsilon)$       251
$[\mathcal{M}(P,g)]_{\delta}$ , $\delta$ -approximation to the fundamental class of $\mathcal{M}(P,g)$ in $X_{\delta}(P,g)$       260
$\bar{\mu}$ , extended $\mu$ -map      272
$\bar{\mu}^{st}$ , extended $\mu$ -map defined on the stable elements      271
$\chi(\pi, SU(2))$ , character variety of representations of it in SU(2)      366
$\delta$ -approximation to the fundamental class      260—262
$\Delta_{T}$ , smooth divisor representing $\mu([T])$ and lying in an arbitrarily small neighborhood of $\overline{D}_{T}(P,g)$       268
$\equiv$ , linear equivalence of divisors      11
$\Gamma(V)$ , group of units in $C_{+}(V)$ of norm one      375
$\gamma_{c,I} (M)$ , generalized Donaldson polynomial for M      411 412
$\gamma_{c} (M, \beta)$ , restricted Donaldson polynomial for M      278
$\Gamma_{\Delta}$ , group generated by the reflections in the set $\Delta$       185 401
$\kappa(S)$ , the Kodaira dimension of S      19
$\lambda_{A}$ , the operator $(\nabla^{*}_{A}, \nabla^{+}_{A})$       238
$\lambda_{c,i}(M,\beta)$ , coefficients of the dual element to $\mathfrak{p}$ in the expansion of $\tilde{\gamma}_{c}(M,\beta)$       278
$\mathbb{S}^{\pm}$ , the bundles of plus and minus spinors      235 376
$\mathcal{A}(P)$ , space of all irreducible $L_{2}^{2}$ connections on the principal bundle P      231
$\mathcal{A}^{0,1}(V)$ , space of all simple $L_{2}^{2}(0,1)$ -connections on the vector bundle V      293
$\mathcal{A}^{0,1}_{\infty}(V)$ , space of all simple $C^{\infty} (0,1)$ -connections on the vector bundle V      283
$\mathcal{A}_{\infty}(P)$ , space of all irreducible $C^{\infty}$ connections on the principal bundle P      230
$\mathcal{B}$ , sheaf of holomorphic cross-sections of the elliptic surface B      77
$\mathcal{C} = \{c_{t}|t \geq 1\}$ , group of conformal contractions of $S^{4}$       251
$\mathcal{F}(J,G)$ , the set of elliptic surfaces without multiple fibers with the invariants J and G      76
$\mathcal{G}(P)$ , the $L^{2}_{3}$ -gauge group of the bundle F      231
$\mathcal{G}(P)_{0}$ , the based gauge group of the bundle F      233
$\mathcal{G}^{\mathds{C},0}$ , the $L^{2}_{3}$ based complex gauge group      330
$\mathcal{G}^{\mathds{C}}$ , the $L^{2}_{3}$ complex gauge group      293
$\mathcal{G}_{\infty}^{\mathds{C}}$ , the complex gauge group of $C^{\infty}$ bundle isomorphisms of the vector bundle V      285
$\mathcal{H}^{0,q}(ad\ V)$ , $\mathcal{H}^{0,q}(End\ V)$ , harmonic forms for the elliptic complex $(\Omega^{0,\bullet}(M; ad\ V), \overline{\partial})$ or $(\Omega^{0,\bullet}(M; End\ V), \overline{\partial})$       294
$\mathcal{H}^{1}(ad\ P)$ , $\mathcal{H}^{2}_{+}(ad\ P)$ , harmonic forms for the elliptic complex $E^{+}(A)$       324
$\mathcal{I}(N)$ , generalized connections whose singular support meets N      263
$\mathcal{J}$ , the subsheaf of $\mathcal{B}$ consisting of holomorphic sections of $\pi$ passing through the identity components of the reducible fibers      82
$\mathcal{J}_{S}$ , the sheaf $R^{1}\pi_{*}\mathcal{O}_{S}/R^{1}\pi_{*}\mathds{Z}_{S}$ on the elliptic surface S      85
$\mathcal{K}(V)$ , the Kuranishi model for the space of deformations of the complex structure on V      295
$\mathcal{M}(P,g)$ , the moduli space of all irreducible g-ASD connections on P modulo gauge equivalence      236
$\mathcal{M}(P,\lambda)$ , the parametrized moduli space of all $g_{t}-ASD$ connections on P where $\lambda$ is the path $\{g_{t}\}$       239
$\mathcal{M}^{0}(P,g)$ , the based moduli space of all g-ASD connections on P      237
$\mathcal{N}_{\delta}(P, g)$ , the image of $\widetilde{\mathcal{N}}_{\delta}(P, g)$ in $\widehat{\mathcal{X}}(P)$       256
$\mathcal{R}(N)$ , reducible ASD connections on the negative definite manifold N      431
$\mathcal{R}(\pi, G)$ , variety of representations of n in the Lie group G      366
$\mathcal{X}(P)$ , space of irreducible $L_{2}^{2}$ connections on P modulo gauge equivalence      232
$\mathcal{X}^{0}(P)$ , $\widehat{\mathcal{X}}^{0}(P)$ , based versions of $\mathcal{X}(P)$ and $\widehat{\mathcal{X}}(P)$       233
$\mathcal{X}_{\infty}(P)$ , space of irreducible $C^{\infty}$ connections on P modulo gauge equivalence      230
$\mathcal{Z}_{c}(C,\theta)$ , the divisor on $\mathfrak{M}_{c}(S,L)$ corresponding to the smooth curve $C \subset S$ and the theta characteristic $\theta$ on C      344 345
$\mathcal{Z}_{c}^{0}(C,\theta)$ , the divisor $\mathfrak{M}_{c}^{0}(S,L)$ corresponding to $\mathcal{Z}_{c}(C,\theta)$       344
$\mathfrak{C}$ , universal elliptic curve over $\mathfrak{H}$       37
$\mathfrak{H}$ , the upper half plane      36
$\mathfrak{H}_{0}$ , $\mathfrak{H}\ -\ PSL(2, \mathds{Z}) \cdot \{0,1728\}$       40
$\mathfrak{M}(C)$ , moduli space of stable bundles of degree zero on C      356
$\mathfrak{M}^{hol}(V)$ , the set of simple holomorphic structures on V      294
$\mathfrak{M}^{sch}$ , scheme version of $\mathfrak{M}_{c,S,L}$       337
$\mathfrak{M}_{0}(C)$ , subset of $\mathfrak{M}(C)$ of bundles with trivial determinant      356
$\mathfrak{M}_{c}(S,L)$ , the moduli space of L-stable rank two holomorphic bundles with $c_{1} = 0$ and $c_{2} = c$       328
$\mathfrak{M}_{c}^{0}(S,L)$ , the based moduli space corresponding to $\mathfrak{M}_{c}(S,L)$       330
$\mathfrak{O}(P)$ , $\mathfrak{O}^{'}(P)$ , sets of generic metrics      237 249
$\mathfrak{p}$ , the image of 1 under the $\mu$ -map      269
$\mathfrak{p}_{\Sigma}$ , the restriction of the extension of $\mathfrak{p}$ to a stratum $\Sigma$       270
$\mathfrak{S}(n_{1},...,n_{t})$ , the largest subgroup of the permutation group of the factors preserving the multiplicities      252
$\mathfrak{S}_{n}$ , the symmetric group on n letters      68
$\mathfrak{X}$ , universal cover of neighborhood of a $I_{k}$ fiber      54
$\mu$ -map      226—229 233—235 340—345 370 371 374 428—431 433 444 461 477—479 486 487 490
$\mu$ -map, extension of      228 263—273
$\mu(V)$ , normalized degree or slope of the holomorphic bundle V with respect to a fixed Kaehler class or ample line bundle      322
$\mu(\alpha)$ , the map $H_{4-i}(M;\mathds{Z}) \rightarrow H^{i}(\mathcal{X}(P);\mathds{Z})$ defined by slant product $-\frac{1}{4}(\tilde{p}_{1}/\alpha)$       233
$\mu^{0}_{T}$ , SO(3)-equivariant class in $H^{i}(\mathcal{X}^{0}(P|T))$ , where T is an embedded 2-manifold      235
$\nabla_{A}$ , differential operator associated to the connection A      231
$\overline{D}_{T}(P,g)$ , the subset of $X_{\delta}(P,g)$ such that either the background connection lies in $D_{T}$ or the singular support meets T      268
$\overline{H}_{2}(M;\mathds{Z})$ , $H_{2}(M; \mathds{Z})$ /Torsion      12
$\overline{\mathfrak{M}}(C)$ , compact moduli space of equivalence classes of semistable bundles of degree zero on C      357
$\overline{\mathfrak{M}}_{0}(C)$ , subset of $\overline{\mathfrak{M}}(C)$ of bundles with trivial determinant      357
$\pi_{1}^{orb} (C, t)$ , the orbifold fundamental group of C      145
$\sigma$ , the real spinor norm      397
$\Sigma_{top}$ , the top stratum $\mathcal{M}(P, g)$ of X(P,g)      261
$\textbf{S}$ , all complex surfaces S such that $\kappa(S) \geq 0$ or $\kappa(S) = -\infty$ and S is algebraic or is deformation equivalent to a (possibly blown up) Hopf surface      221
$\Theta$ , the theta divisor of a Jacobian      345
$\tilde{p}_{1}$ , first Pontrjagin class of the universal SO(3) bundle over $\mathcal{X}(P)\times M$       232
$\tilde{\gamma}_{c} (M, \beta)$ , Donaldson polynomial for M      226 277
$\tilde{\gamma}_{c}^{st} (M, \beta)$ , stable Donaldson polynomial for M      271 273
$\tilde{\jmath}$ , the classical j-function on the upper half plane      37
$\tilde{\lambda}_{c,N,I}(M,\beta)$ , generalized polynomial invariants arising from the connected sum with the negative definite manifold N      426

$\vartheta$ , a theta function with characteristic      345
$\widehat{\mathcal{A}}(P)$ , space of all $L_{2}^{2}$ connections on the principal bundle P      230
$\widehat{\mathcal{A}}^{0,1}(V)$ , space of all $L_{2}^{2}(0,1)$ -connections on the vector bundle V      293
$\widehat{\mathcal{A}}^{0,1}_{\infty}(V)$ , space of all $C^{\infty} (0,1)$ -connections on the vector bundle V      283
$\widehat{\mathcal{A}}_{\infty}(P)$ , space of all $C^{\infty}$ connections on the principal bundle P      230
$\widehat{\mathcal{M}}(P, g)$ , the moduli space of all g-ASD connections on P modulo gauge equivalence      236
$\widehat{\mathcal{X}}_{\infty}(P)$ , space of all $L_{2}^{2}$ connections on P modulo gauge equivalence      231
$\widehat{\mathcal{X}}_{\infty}(P)$ , space of all connections on P modulo gauge equivalence      230
$\widehat{\mathfrak{M}}^{hol}(V)$ , the set of all holomorphic structures on V (usually assumed to have trivial determinant)      285
$\widehat{\mathfrak{M}}^{hol}(V)_{0}$ , the set of holomorphic structures on V with trivial determinant      301
$\widetilde{\mathcal{M}}(P,g)$ , the moduli space of all g-ASD connections on P      236
$\widetilde{\mathcal{N}}_{\delta}(P, g)$ , almost ASD connections on P which are almost flat away from certain points of concentrated curvature, and which lie in the span of the eigenvectors with small eigenvalues for the operator $\nabla^{+}_{A}\circ(\nabla^{+}_{A})^{*}$       255
$_{m}I_{n}$ , a multiple fiber whose reduction is a cycle of n rational curves      35
${\not{\partial}}$ , the Dirac operator      235
${\not{\partial}}_{A}$ , the Dirac operator coupled to the connection A      235
$—E_{8}$ , the intersection form corresponding to the negative of the matrix for the root system $E_{8}$       180
$—\widetilde{E}_{8}$ , the intersection form corresponding to the negative of the matrix for the extended root system $\widetilde{E}_{8}$       181 182
A(M), automorphisms of $H_{2}(M)$ preserving the quadratic form $q_{M}$ of M      12
A(M, k), automorphisms of the quadratic form of M preserving k      393
ad P, adjoint bundle associated to the principal bundle P      230
ad V, vector bundle of trace zero endomorphisms of the vector bundle V      300
Adjunction formula      194 418 454 464
Almost complex structure      282 284 308 312—313 314
Analytic function on a Banach space      285—293
Anti-self dual (ASD)      see "Connection anti-self-dual"
Artin ring      95 337 350
Artin, M.      32
ASD connections      see "Connection anti-self-dual"
ASD Yang — Mills equations      see "Yang — Mills equations"
Atiyah — Hitchin — Singer deformation complex      237 319
Atiyah — Singer determinant      see "Determinant line bundle Atiyah
Atiyah's theorem on vector bundles over elliptic curves      447 448 452 456
Atiyah, M.      137
Averbuh, B.G.      32
B(g,d), the set of isomorphism classes of elliptic surfaces S with a section with Euler number 12d over a base of genus g      63
Background connection      228 229 244—247 249—251 253—255 257—261 263 265 266 430 434—436
Base change      33 38 47 53 95 98 99 115 116 163 164 338 382 452 462 465 466 482 483 488
Basic member      76 85 93 205
Basic surface      see "Elliptic surface basic"
Bauer, S.      223 497
Bianchi identity      284 294
Bismut — Freed determinant      374
Bismut — Gillet — Soule determinant      374 389—392
Block      71—75
Blowing down      17 21 24—27
Blowing down in families      21 24—27 35
Blowing up      17 19 131 132 163
Blowup      4 5 10 17—20 23 27 28 36 51 59 131 132 137 154—157 163 164 181 221—225 394 411—416 418 426 491—498
Bogomolov — Miyaoka — Yau inequality      30 494 495
Bogomolov's inequality      367
Bogomolov, F.      366
Bombieri's theorem on the canonical map      33
Bombieri, E.      33
Borel measure      240
Botany      23
Bott, R.      137
Bounded homogeneous polynomial      285
Br B, the Brauer group of B      86
Brauer group      86 109 335
Bridge      72—75
Brieskorn, E.      33 115
Brussee, R.      499
C(V), Clifford algebra of V      374
c-generic      339
c-stable      271 276
c-suitable      436 438 446—448 450 451 453 454 468 476 477
Canonical bundle      2 10 11 16—20 24 25 130 160 341 343 376 394 406 410 418 450 477
Canonical bundle formula for an elliptic surface      16 36 49 50 129 130 454 464 475
Cartan matrix      179 187
Cartan's privileged neighborhood theorem      298
Case (A)      447 448 451 453—455 469 479 480 485 497
Case (B)      448 453—456 480 481
Castelnuovo — deFranchis theorem      20 30 494
Castelnuovo — Enriques theorem      20
Castelnuovo's theorem      2 25
Categorical quotient      362 364
Christoffel symbol      378
Clifford algebra      374 375
Clifford multiplication      375—377
Clifford's theorem      360
Closure of modules theorem      288 289
Compatible lift      41—47 67
Completion of the moduli space      239—246
Completion of the moduli space, thickened      247 260—263
Complex space      11
Complex space, defined by a Fredholm map      290—293
Complex space, defined by a Fredholm section      265 292 293
Complex torus      22 30—33 92 131 154 155 199 209 214 222 224 444 458 494 495
Cone bundle      228 247 251 253 255 258—260 265 271
Cone structure      248 251 253 258
Conformal length      432
Conjugate complex manifold      5 139 206 409
Connected sum      2 9 10 12 161 229 271 356 394 411—414 416—419 425 426 432 433 435
Connection, (0,1)-      283—285 294 300 301 307 314 324 327 331
Connection, background      228 229 244—247 249—251 253—255 257—261 263 265 266 430 434—436
Connection, compatible with the complex structure      280—283 313 320 323 333
Connection, Ehresmann      280 284 314
Connection, flat      88 249 251 366 369 379
Connection, Hermite — Einstein      323
Connection, Hermitian      281 323
Connection, integrable      284 285
Connection, irreducible      226 227 230 231 234 236 237 249 256 271 279 324—327 330 347 365 429 431 438
Connection, Levi-Civita      376
Connection, product      240 243 249 256 258
Connection, reducible      231 246 249 250 257 274 338 348 366 429—432 436 438—440
Connection, trivial      228 238 243 246 247 255—260 348 370 373 430 431 433 435
Connections, based, space of gauge equivalence classes      233 431
Connections, space of gauge equivalence classes      226 230—234
Contains in the sense of complex spaces      288
Curvature      230 232 282 283
Curvature, (0,2)-      284 285 293
Curvature, concentrated      228 254
Cyclic monodromy      195—197 201 202 205 209 210 214 215
d(c), one-half the expected dimension of the moduli space, namely $4c-3(1+b^{+}_{2})/2$       226
D(M), the subgroup of A(M) induced by $Diff^{+} M$       12
D(M,k), the subgroup of D(M) of elements fixing k      393 405
D*(M), the subgroup of D(M) of elements of real spinor norm one      393
Dabrowski, K.      133
Deformation equivalence      4 5 10 14—22 25 28 29 31—34 57 61 81 93 103 138—140 157 201 221—224 409 442 445 497
Deformation equivalence through elliptic surfaces      35 57 64—67 79 81 82 103—107 110—132 158 159 201 205—209 211 215
Deformation invariance of Kodaira dimension      20 26 27
Deformation invariance of the plurigenera      20 24 26 27 128—130
Deformation type      4—7 16 17 28 195 497
Deformation, unobstructed      301
Degree, local, for a Fredholm map of index zero      352 355
Dehn twist      167
Dehn — Nielsen theorem      146—154
Deligne — Mumford Theorem      125
Deligne, P.      401
Descent conditions      473
det $R_{\pi_{*}}$ , the holomorphic determinant line bundle      383
Determinant line bundle      238 340 352 355 374
Determinant line bundle, Atiyah — Singer      235 374 385—389 391
Determinant line bundle, Bismut — Freed      374
Determinant line bundle, Bismut — Gillet — Soule      374 389—392
Determinant line bundle, holomorphic      341 342 344 364 366 374 379—385 387—389 391
Diffeomorphism group, big      9 393 394 405—409 413 415 416 418 420 425 427 490 499
Diffeomorphism group, big, Donaldson polynomial of a 4-manifold with      9 393 406—408 490 499
Dirac operator      235 268 269 274 340 341 346—348 374—379
Directional derivative      420
Distribution, horizontal      232 280 282 331
Distribution, integrable      308
Distribution, involutive      308
Div, div, the zero set of the natural section of the inverse of the determinant line bundle      384
Dolgachev, I.      16 75 86
Donaldson polynomial invariant      4 226 227
Donaldson polynomial invariant, full      229 230 276 278
Donaldson polynomial invariant, generalized      411—413
Donaldson polynomial invariant, restricted      278
Donaldson polynomial invariant, stable      229 271—273 276

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