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Huybrechts D., Lehn M. — The Geometry of Moduli Spaces of Sheaves
Huybrechts D., Lehn M. — The Geometry of Moduli Spaces of Sheaves



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Название: The Geometry of Moduli Spaces of Sheaves

Авторы: Huybrechts D., Lehn M.

Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 269

Добавлена в каталог: 06.05.2005

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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 $M^s$      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 $\mathbb{P}^1$      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 $\mu$-semistable sheaves      190
Moduli space of coherent sheaves      80 91
Moduli space of coherent sheaves on $\mathbb{P}^2$      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 $\mu$-semistable sheaves, Bogomolov's Theorems      170—177
Restriction to hypersurface of $\mu$-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 $S_{k,c}$      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), $\mu$-      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 $\mathbb{P}^1$      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 $\cdots$
Symmetric powers      67
Symmetric product      91
Symplectic structure      215 see
Symplectic structure, closed      215
Symplectic structure, non-degenerate      215 228
Tangent bundle of $\mathbb{P}^n$ 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 $\mathbb{P}^1$      14
Vector bundle on $\mathbb{P}^n$      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
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