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Huybrechts D. — Fourier-Mukai Transforms in Algebraic Geometry
Huybrechts D. — Fourier-Mukai Transforms in Algebraic Geometry



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Название: Fourier-Mukai Transforms in Algebraic Geometry

Автор: Huybrechts D.

Аннотация:

This seminal text on Fourier-Mukai Transforms in Algebraic Geometry by a leading researcher and expositor is based on a course given at the Institut de Mathematiques de Jussieu in 2004 and 2005. Aimed at postgraduate students with a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. Including notions from other areas, e.g. singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs are given and exercises aid the reader throughout.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 312

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A_m$-configuration      175
$\mathbb{P}^n$-object      173
Abelian surface      272 276
Abelian variety      192
Abelian variety, dual of      196 199
Abelian variety, line bundle on      197
Abelian variety, polarized      200
Abelian variety, polarized, principally      201 207 208
Algebraic symplectic variety      173 245 264
Ample sequence      59 69 101 102 110 112
Appell — Humbert datum      197
Autoequivalence      18 99 168
Autoequivalence, group of      18 173 178 218
Autoequivalence, group of, for abelian variety      211 223
Autoequivalence, group of, for Fano variety      100
Autoequivalence, group of, for K3 surface      239 295
Base change      85 202 206 207 268
Beilinson spectral sequence      179 181
Blow-up      147 252
Braid group      175
Braid group, action      178
Calabi — Yau manifold      150 169 170 173 179 184 289
Canonical bundle      67
Canonical bundle, (anti-)ample      93 95
Canonical bundle, (anti-)ampleunder derived equivalence      92 149
Canonical bundle, nef, under derived equivalence      146 273
Canonical bundle, order of under derived equivalence      90 273
Canonical bundle, under derived equivalence      90
Canonical cover      162 272 276 280
Canonical ring, of line bundle      151
Canonical ring, of variety      151
Canonical ring, under derived equivalence      137
Cartan — Eilenberg resolution      56
Category, abelian      4
Category, additive      3
Category, derived      30 36
Category, derived, bounded      37
Category, derived, indecomposable      66
Category, derived, of scheme      62
Category, equivalent      2
Category, homotopy      31 46
Category, homotopy, of injectives      41
Category, linear      3
Category, of complexes      28
Category, sub-adapted      48
Category, sub-admissible      16 25
Category, sub-orthogonal complement of      16
Category, sub-thick      42
Category, sub-triangulated      16
Category, triangulated      11
Category, triangulated, decomposition of      22
Category, triangulated, equivalence of      18
Category, triangulated, indecomposable      22
Chern character      126
Complex, acyclic      29 50
Complex, bounded      37
Complex, cohomology of      29
Complex, double      54
Complex, double, filtration of total      54
Convolution      205
Crepant resolution      271 286
D-equivalence      62 150 287 291
Decomposition      22
Decomposition, semi-orthogonal      25 184 256 257 260 261
Derived equivalence      62
Derived equivalence, Fourier — Mukai transform      120
Derived equivalence, K3 surfaces      234
Derived equivalence, of abelian varieties      214 215 219
Derived equivalence, of curves      99 135 170
Derived equivalence, of elliptic curves      135 179
Derived equivalence, of Fano varieties      95
Derived equivalence, of surfaces      272
Direct image      6 44 72 74 83 86
Direct image, higher      72
Direct image, K-theoretic      124
Distinguished triangle      12
Dual      78
Dual, double      84
Dual, of structure sheaf of subvariety      89
Dualizing functor      87
Dualizing sheaf      67
Enriques surface      276 280
EQUIVALENCE      2 21 22
Equivalence, exact      18
Equivalence, of triangulated categories      18
Euler number of K3 surface      229
Euler number, under derived Equivalence      130 273
Exceptional object      24 181 184
Exceptional sequence      24
Exceptional sequence, full      24 181
Exceptional sequence, strong      183
Fermat surface      229
Flip      259
FLOP      259
Fourier — Mukai kernel      113
Fourier — Mukai kernel, for abelian Fourier — Mukai kernel, varieties      222
Fourier — Mukai kernel, uniqueness of      121
Fourier — Mukai partner      114 286
Fourier — Mukai partner, finiteness of      215 286
Fourier — Mukai transform      113
Fourier — Mukai transform, adjoints of      116
Fourier — Mukai transform, equivalence      159 161
Fourier — Mukai transform, exact      114
Fourier — Mukai transform, fully faithful      154 159
Fourier — Mukai transform, K-theoretic      125
Fourier — Mukai transform, kernel of      113
Fourier — Mukai transform, on Chow groups      126
Fourier — Mukai transform, on cohomology      126
Fourier — Mukai transform, product of      158 161
Functor, (quasi-)inverse      2
Functor, additive      3
Functor, adjoint, left      5 6 9 11 15
Functor, adjoint, right      5 6 9 11 15
Functor, derived, higher      47
Functor, derived, right      46
Functor, dualizing      87
Functor, exact      5 14 37 43 45 46
Functor, exact, left      5 6 44 45 47 48 71
Functor, exact, right      5 6 45 78
Functor, faithful      1
Functor, full      1
Functor, fully faithful      21 22
Functor, fully faithful, via spanning class      20 101
Functor, isomorphism      1
Functor, linear      3
Functor, morphism      1
Global Torelli theorem for Enriques surfaces      280
Global Torelli theorem for K3 surfaces      230
Grothendieck group      124 292 293
Grothendieck — Riemann — Roch formula      127 232
Grothendieck — Verdier duality      67 86 116
Hilbert scheme      191
Hirzebruch — Riemann — Roch formula      127
Hochschild cohomology      131 139 140 218
Hodge isometry      220 230 234
Hodge isometry, orientation preserving      237
Hodge structure      130 297
Homological dimension, finite      59
Hypercohomology      71
Integral functor      113 see
Inverse image      45 80 83
Isogeny      194 200 206
Isogeny, degree of      194
K-equivalence      150 287 291
K3 surface      228 272 276 293
K3 surface, derived equivalence of      233
K3 surface, period of      230
Kahler cone      230
Kodaira dimension      151
Kodaira dimension, numerical      152
Kodaira dimension, numerical, under derived equivalence      146 147 273
Kodaira dimension, under derived equivalence      137 273
Kodaira's lemma      148
Koszul complex      180 250
Kuanneth formula      86 158 196 198 262
Kummer surface      229
Line bundle, nef      151
localization      36
Mapping cone      33
Moduli space, coarse      241
Moduli space, fine      243 282
Morphism of complexes      28
Morphism of complexes, homotopically equivalent      31
Morphism of complexes, homotopy      31
Mukai flop, stratified      270
Mukai pairing      132 172 267
Mukai pairing, for K3 surface      231
Mukai vector      127 172 231
Mutation      184
Object, acyclic      47
Object, injective      5
Object, injective, enough      41 45 50 57
Object, invertible      93
Object, point like      91
Object, projective      5
Object, projective, enough      40 50
Object, simple      91
Picard functor      199
Picard group      140 195 218
Picard number, under derived equivalence      273
Poincare bundle      197
Poincare bundle, as Fourier — Mukai kernel      201
Poincare bundle, Chern class of      198
Poincare bundle, versus Poincare duality      204
Poincare duality      203 204
Projection formula      83 126 249 257 268
Projective bundle      254
Pull-back      6 45 80 86
Pull-back, K-theoretic      124
Pull-back, on cohomology      126
Quasi-isomorphism (qis)      29
Resolution, Cartan — Eilenberg      56
Resolution, injective      39
Resolution, injective, of sheaf      63
Resolution, projective      39
See-saw principle      194
Serre duality      67 87 116
Serre functor      9 23
Serre functor for varieties      67
Serre functor is exact      18
Sheaf, dual of      78
Sheaf, flabby      73
Sheaf, injective      63 73
Sheaf, stable      240
Shift functor      12 28
Slope function      292
Spanning class      20
Spanning class, ample sequence      59 101
Spanning class, for spherical object      169
Spanning class, of closed points      69
Spanning class, of line bundles      59 69
Spectral sequence      52
Spectral sequence, Beilinson      181
Spectral sequence, Leray      74
Spherical object      166 184 191 258
Spherical object, $A_m$-conflguration of      175
Spherical object, on Calabi — Yau manifold      170
Spherical object, on curve      170
Spherical twist      167 234
Spherical twist, cohomological      171 172
Spherical twist, equivalence      168
Stability condition      292
Stable sheaf      240
Stable sheaf, moduli space of      241
Support      65
Support, of dual      84
Support, of restriction      81
Surface, canonical model of      275
Surface, elliptic      276 282 284
Surface, hyperelliptic      276
Surface, minimal      274
Surface, minimal model of      274
Surface, of general type      275
Surface, rational      274
Surface, ruled      274
t-structure      292
T-structure, heart of      292
Tensor product of complexes      79
Theorem of the Cube      194
Theorem of the Square      195
Todd class      127
Trace      77
Triangle, distinguished      36
Yoneda Lemma      2
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