|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Huybrechts D., Lehn M. — The Geometry of Moduli Spaces of Sheaves |
|
|
|
| Предметный указатель |
Action of an algebraic group 81
Albanese morphism 225 231
Albanese variety 126 225
Albanses morphism 229
Ample line bundle on moduli space 184
Ample pseudo- divisor 64
Ample vector bundle 64
Ample vector bundle, tensor product of 66
Ampleness criterion for Carrier divisors 64
Ampleness criterion for vector bundles on curves 65
Annihilator ideal sheaf 3
Atiyah class 218 229
Auslander — Buchsbaum formula 4
Bertini Theorem 8
Bogomolov Inequality 72 171—173
Bogomolov Restriction Theorem 174
Boundary 201
Boundedness Grothendieck Lemma 29
Boundedness Kleiman Criterion 29
Boundedness of a family 28
Boundedness of semistable sheaves 70
Boundedness of semistable sheaves on curves 28
Canonical class of moduli space 195
Cayley — Bacharach property 123
Chamber see wall
Cohomology class, primitive 151
Connection 61 218
Cup product 216
Deformation theory 49
Descent 87
Determinant bundle 9 37
Determinant bundle of a family 178
Determinant bundle on the moduli space 180
Determinantal variety 121
Differentials with logarithmic poles 129
Dimension estimate 199—213
Dimension estimate for  101
Dimension estimate for flag schemes 54
Dimension estimate for Quot- scheme 44
Dimension estimate for R 104
Dimension estimate general 53
Dimension of a sheaf 3
Dimension, expected of moduli space 103
Discriminant 71
Donaldson — Uhlenbeck compactification 195
Elementary transformation 129 137
Enriques classification 235
Equivariant morphism 81
Euler characteristic of a pair of sheaves 141
Euler characteristic of a sheaf 9
Extension, small 49
Extension, universal 37
Exterior powers 67
Family, bounded 28
Family, flat 32
Family, quasi-universal 105
Family, universal 105
Family, universal, existence of 107
Filtration, Harder — Narasimhan 16 26
Filtration, Harder — Narasimhan, relative 46
Filtration, Harder — Narasimhan, under base field extension 17
Filtration, Jordan — Holder 22 26
Filtration, torsion 3
Finite coverings 62
Flag-schemes 48
Flatness criterion 33
Flenner, Theorem of 161
Form, one- 223—226
Form, two- 215 223—226 232
Form, two-, non-degeneracy of 226—229
Frame bundle, (projective) 83
Framed module 111
Functor category 38
Functor, (universally) corepresentable 38
Functor, pro-represented 53 101
Functor, representable 38
Geometric invariant theory 85
Gieseker's construction 109
Gieseker-stability 13
git see Geometric Invariant Theory
Grassmannian 38
Grassmannian, tangent bundle of 44
Grauert — Mulich Theorem 57 59 61
Grothendieck group 36 178
Grothendieck Lemma 29
Grothendieck — Riemann — Roch formula 195
Grothendieck's Theorem 1.3.1 on vector bundles on  14
Group, algebraic 81
Group, reductive 85
Hermite — Einstein metric 67
Hilbert polynomial 9
Hilbert polynomial, reduced 10
Hilbert scheme 41 92
Hilbert scheme , Kodaira dimension 231
Hilbert scheme of K3 surface 150 156 238
Hilbert scheme of K3 surface, Hodge structure 155
Hilbert scheme, smoothness 104
Hilbert — Mumford criterion 86 96
Hilbert-to-Chow morphism 92
Hodge index theorem 132 172
Hodge structure of irreducible symplectic manifold 155
Hodge structure of moduli space 148
Hodge structure of surface 146
Invariant morphism 82
Irreducibility of moduli space 203
Irreducibility of Quot-scheme 157
Isotropic vector 146
Isotropy subgroup 82
K-groups see Grothendieck group
Kleiman Criterion 29
Kleiman's transversality theorem 121
Kobayashi — Hitchin correspondence 67
Kodaira dimension 230
Kodaira dimension of Hilbert scheme 231
Kodaira dimension of moduli space 232
Kodaira — Spencer map 221
Langton, Theorem of 55 189
Le Potier-Simpson Estimate 68
Limit point 86 96
Linear determinant 92
Linearization of a group action 84
Linearization of a sheaf 83
Local complete intersection 44 103
Local complete intersection, general criterion 53
Luna's Etale Slice Theorem 86 113
Manifold, hyperkahler 150
Manifold, irreducible symplectic 150
Mehta, Theorem of- and Ramanathan 164
Moduli functor 80
Moduli space of  -semistable sheaves 190
Moduli space of coherent sheaves 80 91
Moduli space of coherent sheaves on  235
Moduli space of coherent sheaves on a curve 100 103 187 195 204
Moduli space of coherent sheaves on abelian surface 228 236
Moduli space of coherent sheaves on elliptic K3 surface 135 152 239
Moduli space of coherent sheaves on elliptic surface 139 237 239
Moduli space of coherent sheaves on Enriques surface 237
Moduli space of coherent sheaves on fibred surface 131
| Moduli space of coherent sheaves on hyperelliptic surface 237
Moduli space of coherent sheaves on irregular surface 231
Moduli space of coherent sheaves on K3 surface 133 151 156 228 236 238
Moduli space of coherent sheaves on rational surface 235
Moduli space of coherent sheaves on ruled surface 132 235
Moduli space of coherent sheaves on surface of general type 228 232 237
Moduli space of coherent sheaves, Hodge structure 148 156
Moduli space of coherent sheaves, two-dimensional 144
Moduli space of coherent sheaves, zero-dimensional 143
Moduli space of framed modules 112
Moduli space of polarized k3 surfaces 152
Moduli space of simple sheaves 118
Moduli space, canonical class of 195
Moduli space, differential forms on 225
Moduli space, fine 105
Moduli space, local properties of 101
Moduli space, tangent bundle of 222
Mukai vector 142
Multiplicity of a sheaf 10
Mumford Criterion see Hilbert — Mumford Crite-Criterion
Mumford — Castelnuovo regularity 28
Mumford — Takemoto-stability 13
Nakai criterion 64
Nef divisor 64
Newton polynomial 219
Normality of hyperplane section 8
Normality of moduli space 202
Numerically effective divisor see nef divisor
Obstruction 43
Obstruction for deformation of a flag of subsheaves 51
Obstruction for deformation of a sheaf 50
Obstruction theory 53
Obstruction, comparison of deformation- 51
Obstruction, theory 49
Open property 35 45
Openness of semistability 45
Orthogonal 178
Period point 155
Picard group of moduli space 180 182
Picard group, equivariant 87 179 182
Pluecker embedding 42
Point, (semi)stable 85
Point, good see good sheaf
Point, properly semistable 85
Poisson structure 229
Polarization, change of 114
Polarization, suitable 131
Principal G-bundle 83 91
Pro-represented functor see functor
Pseudo-ample divisor 64
Purity of a sheaf 3
Quadratic form 155 156
Quot-scheme 39
Quotient, (universal) categorical 82
Quotient, (universal) good 82
Ramanathan, Theorem of Mehta and 164
Reflexive hull of a sheaf 6
Regular section 7
Regular sequence 4 9 28 68
Regularity see Mumford-Castelnuovo -
Resolution, Flenner's Theorem 160—164
Resolution, injective 48
Resolution, locally free 36
Resolution, The Theorem of Mehta — Ramanathan 164—170
Restriction of -semistable sheaves, Bogomolov's Theorems 170—177
Restriction to hypersurface of -semistable sheaf 58—62
Restriction to hypersurface of pure sheaf 8
Restriction to hypersurface of reflexive sheaf 8
S-equivalence 22 80 91
Saturation of a subsheaf 4
Semistability of exterior and symmetric powers 67
Semistability of tensor product 61
Semistability, behaviour under finite coverings 63
Serre construction see Serre correspondence
Serre correspondence 123 136 238
Serre correspondence, higher rank 128
Serre subcategory 24
Serre's condition  4
Sheaf, degree 13
Sheaf, dual of 5
Sheaf, good 202
Sheaf, m-regular 27
Sheaf, maximal destabilizing sub- 16
Sheaf, polystable 23 63 67
Sheaf, pure 3 45
Sheaf, rank of 10
Sheaf, regularity of 28
Sheaf, simple 12 45
Sheaf, slope of 14
Sheaf, stable(semi) 11 25
Sheaf, stable(semi), - 14 26
Sheaf, stable(semi), c- 74 207
Sheaf, stable(semi), geometrically 12 23
Sheaf, stable(semi), properly 80 108
Sheaf,reflexive 6
Singular points of a sheaf 9
slope see sheaf
Smoothness criterion 102
Smoothness of Hilbert scheme 104
Smoothness, generic, of moduli space 202
Socle 23
Socle of a torsion sheaf 157
Socle, extended 23
Splitting of vector bundles on 14
Stabilizer see isotropy subgroup
Stratification, double-dual 210
Stratification, flattening 33
Support of a sheaf 3
Surface, abelian etc. see moduli space of coherent sheaves on 
Symmetric powers 67
Symmetric product 91
Symplectic structure 215 see
Symplectic structure, closed 215
Symplectic structure, non-degenerate 215 228
Tangent bundle of  is stable 21
Tangent bundle of Grassmann variety 44
Tangent bundle of moduli space 222
Trace map 63 102 113 217
Traceless, endomorphisms 102 202
Traceless, extensions 102 202
Traceless, extensions, global bound for 103
Trivialization, universal 85
Variety of general type 231
Variety, rational 230
Variety, unirational 230
Vector bundle on 14
Vector bundle on 19—21
Vector bundle, ample see ample
Vector bundle, globally generated 121
Vector bundle, stable, existence 125 128 130
wall 114 118
Weight, of a Gm -action 96
Yoneda Lemma 38
Zariski tangent space 42
Zariski tangent space of flag scheme 53
Zariski tangent space of Grassmannian 44
Zariski tangent space of moduli space 101
Zariski tangent space of Quot-scheme 44
|
|
|
| Реклама |
|
|
|
|
|
О проекте