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Friedman.R. — Algebraic Surfaces and Holomorphic Vector Bundles
Friedman.R. — Algebraic Surfaces and Holomorphic Vector Bundles

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Название: Algebraic Surfaces and Holomorphic Vector Bundles

Автор: Friedman.R.

Аннотация:

This book covers the theory of algebraic surfaces and holomorphic vector bundles in an integrated manner. It is aimed at graduate students who have had a thorough first-year course in algebraic geometry (at the level of Hartshorne's Algebraic Geometry), as well as more advanced graduate students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology. Many of the results on vector bundles should also be of interest to physicists studying string theory. A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, and are studied in alternate chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, and then the geometry of vector bundles over such surfaces is analyzed. Many of the results on vector bundles appear for the first time in book form, suitable for graduate students. The book also has a strong emphasis on examples, both of surfaces and vector bundles. There are over 100 exercises which form an integral part of the text.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 264

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$T_{p,q,r}$ graph      81
$T_{p,q,r}$ lattice      81
$\mu$-map      205
$\sigma$-Process      59
Abelian surface      see Surface abelian
Abundance theorem      279 293 306
Ad V      99
Adjoint bundle      see Ad V
Adjunction formula      13
Albanese map      118 289
Albanese variety      288
Algebraic function field      271 275
Allowable elementary modification      see Elementary modification allowable
Almost decomposable      2
Ample cone      19
Andreotti, A.      278
Anti-serf-dual connection      see Connection anti-serf-dual
Arithmetic genus      see Genus arithmetic
Artin's criterion      75 80
Atiyah — Singer index theorem      207
Atiyah's theorem on vector bundles      1 33
Atiyah, M.      1
Auslander — Buchsbaum dimension formula      51 199
Barlow surface      see Surface Barlow
Barth, W.      3 162 310
Base point, assigned      69
Base point, infinitely near      69
Base point, simple      69
Base point, unassigned      69
Basic elliptic surface      see Surface elliptic basic
Bauer, S.      240
Big divisor      see Divisor big
Bloch, S.      312
Blowing down      66
Blowing up      59
Bogomolov number      274
Bogomolov — Miyaok — Yau inequality      1 282
Bogomolov's inequality      3 22 107 149 163 245—247 305
Bogomolov, F.      3 245
Bombieri's theorem      79 248
Bombieri, E.      1 248
Botany      282
Brosius, J.E.      3 150 310
Brussee, R.      312
Canonical bundle formula      176
Canonical curve      134 139
Castelnuovo — deFranchis theorem      283 302
Castelnuovo's criterion      1 64—67
Castelnuovo's theorem      278
Catanese, F.      14
Cayley — Bacharach property      40 126
Chambers of type (w,p)      100
Chern class      27—30
Chern class, total      28
Chevalley, C.      275
Chow group      28 312
Chow's theorem      7
Class field theory      271
Class of type (w,p)      100
Classification of threefolds      305
Clifford's theorem      163 256
Coarse moduli space      see Moduli space coarse
Compatible pair      186
Complex torus      see torus
Computation sequence      80 168
Computation sequence, numerically      24 191
Connection      101
Connection matrix      102
Connection, anti-self-dual      105 206
Connection, flat      102
Connection, Hermitian      102
Connection, Hermitian — Einstein      3 104 245
Connection, integrable      102
Connection, irreducible      102
Connection, self-dual      105
Connection, unitary      102
Contraction      66
Cremona transformation      69
Cubic surface      see Surface cubic
Curvature      102
Cusp      14 23 138 173
Deformation theory      155
Degree of a torsion free sheaf      198
Degree, normalized      85
Del Pezzo surface      see Surface del
Depth      51
Desale, U.V.      2
Descent theory      145 265
Destabilizing      86
Div X      9
Divisor      9
Divisor class      10
Divisor, big      20 72
Divisor, effective      9
Divisor, nef      20 72
Dolgachev surface      see surface Dolgachev
Dolgachev, I.      189 278
Donaldson invariant      101 197 203 205
Donaldson polynomial      205
Donaldson polynomial on $P^2$      206
Donaldson — Uhlenbeck — Yau theorem      106 245
Donaldson, S.      3 208 308
Double cover      2 46—50 57
Double point, ordinary      14 23 133 138 173 241
Double point, ordinary, threefold      210 242
Double point, rational      77—78 81—83 128 129 134 138 178 182
Dual complex      75
Dual graph      75 173
Dualizing sheaf      13
Dynkin diagram      173
Effective      see Divisor effective
Eimination of indeterminacy      68
Elementary modification      41—42 55
Elementary modification, allowable      148
Elementary transformation      114 118
Elliptic normal curve      128
Elliptic surface      see Surface elliptic
Embedded resolution      63
Enriques surface      see Surface Eariques
Enriques' theorem      1 280
Enriques, F.      278
Enumerative geometry      2 3
Enumerative geometry, linear      10
Enumerative geometry, numerical      17
Enumerative geometry, of families of vector bundles      153
Euler characteristic      9
Euler characteristic, holomorphic      9
Euler exact sequence      109
Eventually base point free      21 72
Exceptional curve      66—67
Exceptional divisor      59
Expected dimension      158
Extended root system      173
Extremal rays      305
Factorization of birational morphisms      67
Faithfully flat      275
Fernandez del Busto, G.      245
Fibration      167
Fine moduli space      see Moduli space fine
Fintushel, R.      240
Flat connection      see Connection flat
Formal functions theorem      62 65 74
Freedman, M.      278
Fulton, W.      4 28
Fundamental cycle      79—82 191
Galois cohomology      184 185
Galois morphism      272
General type      277; see Surface general
Generic rank      26
Genus drop      14
Genus drop, local      14
Genus, arithmetic      13
Genus, geometric      8
Geography      282
Geometric genus      see Genus geometric
Geometric invariant theory      1 154
Gieseker compactification      206
Gieseker stability      see Stability Gieseker
Gieseker, D.      2 154 245 257 259 307 310
Godeaux surface      see surface Godeaux
Gomez, T.      311
Gomprecht, D.      313
Good generic surface      see Surface good
Good vector bundle      see Vector bundle good
Grauert's contraction theorem      72
Grauert, H.      72
Griffiths, P.      4
Grothendieck — Riemann — Roch theorem      4 29 48 212 213 215
Grothendieck's theorem on vector bundles      1 33
Grothendieck, A.      1 154
GSttsche, L.      206
Harder — Narasimhan filtration      97 112
Harris, J.      4
Hartogs' theorem      60 67
Hartshorne, R.      3 259
Hermitian — Einstein connection      see Connection Hermitian
Hilbert scheme      155 164 204
Hirzebruch signature theorem      9 22
Hodge index theorem      9 16—18 23
Hodge theory      8—9 17
Homological invariant      186
Hoppe, H.-J.      3 310
Horikawa surface      see Surface Horikawa
Horikawa, E.      282
Hulek, K.      3 162 310
Hyperelliptic surface      see Surface hyperelliptic
Infinitely near      63
Intersection pairing      8 11
Irregularity      8
Irregularity, birational invariance of      62 70
Italian algebraic geometry      1 278
J-function      185
Jacobinn elliptic surface      see Surface elliptic Jacobian
Jordan — Hoeder filtration      112 154
K3 surface      see Surface K3
Kaehler identities      105 106
Kaeler manifold      101 103
Kametani, Y.      218
Kawamata — Viehweg vanishing theorem      245
Klein, F.      63
Kobayashi — Hitchin conjecture      3
Kobayashi, S.      3 106
Kodaira classification      7
Kodaira classification of surfaces      278
Kodaira dimension      7 277
Kodaira dimension of the moduli space of bundles      311
Kodaira vanishing theorem      22 247
Kodaira — Spencer class      156
Kodaira, K.      1 70 131 175 176 186 187 189 249
Koszul complex      32
Kotschick, D.      278
Kronheimer. P.      3
Kummer surface      see surface Kummer
Lang, S.      275
Leading coefficient of the Donaldson polynomial      240
Lefschetz theorem on (1,1)-classes      18
Lefschetz theorem on hyperplane sections      22
Leray spectral sequence      4
Leung, N.      3
Li, J.      207 308 310 311
Logarithmic transformation      187
Luebke, M.      3 106
Lueroth problem      287
m-sequence      51
Maruyama, M.      3 154 158 162 307 310
Matsumura, H.      4
Mayer, A.      135
Mehta — Ramanathan restriction theorem      246 309
Mehta, V.B.      246
Minimal model      70—71
Minimal model of a threefold      306
Minimal model, relatively      171
Minimal model, strong      71—72
Minimal surface      see Surface minimal
Miyaoka, Y.      245
Moduli functor      153
Moduli space      153
Moduli space, fine      155
Moishezon, B.      175 189 249
Monads      3
Monoidal transformation      59
Morgan, J.W.      207 240
Mori theory      4 277 279
Mori, S.      4 279 305
Mrowka, T.      3
Mukai, S.      3 310
Multiple fiber      169
Multiplicity      60
Multiplicity of a multiple fiber      169
Mumford's vanishing theorem      22 247
Mumford, D.      1 21 22 72 78 154 246 312
Nagata, M.      91
Nakai — Moishezon criterion      18—21 23
Narasimhan — Seshadri theorem      2 3 105
Narasimhan, M.S.      2 313
Nef divisor      see Divisor nef
Nef, relatively      172
Noether's formula      9 22
Noether's inequality      281
Normalized degree      85; see Degree normalized
Num X      17
Numerically connected      see Connected numerically
Ogg, A.      194
Okonek, C.      278
Orbifold      188
Orbifold fundamental group      188
Ordinary double point      see Double point ordinary
Oriented wall      100
O’Grady, K.      240 310—311
Period map      133 297
Picard number      18
Pidstrigach, V.      278
Plurigenera      9
Plurigenera, birational invariance of      62 70
Poincare duality      8
Poincare line bundle      263
Principal homogeneons space      183
Projection formula      24
Projective dimension      51
Projective tangent cone      60
Projectively normal      128
Proper transform      60
Qin, Z.      163 278
Quot scheme      155
Ramanan, S.      2 313
Ramanathan, A.      246
Ramanujam's lemma      191
Rational double point      see Double point rational
Rational equivalence      28
Rational normal curve      116
Rational ruled surface      see Surface rational
Rational surface singularity      74—78 80—82 138
Reflexive      45 53—54 56
Reider's theorem      249 274
Reider, I.      248
Relative duality      177
Relative Picard variety      263
Relatively minimal model      see Minimal model relatively
Representable functor      153
Riemann — Roch theorem      4
1 2
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