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| Huybrechts D. — Fourier-Mukai Transforms in Algebraic Geometry |
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| Предметный указатель |
 -configuration 175
 -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, -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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