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Ueno K. — Advances in Moduli Theory
Ueno K. — Advances in Moduli Theory

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Название: Advances in Moduli Theory

Автор: Ueno K.

Аннотация:

Shimizu and Ueno (no credentials listed) consider several aspects of the moduli theory from a complex analytic point of view. They provide a brief introduction to the Kodaira-Spencer deformation theory, Torelli's theorem, Hodge theory, and non-abelian conformal theory as formulated by Tsuchiya, Ueno, and Yamada. They also discuss the relation of non-abelian conformal field theory to the moduli of vector bundles on a closed Riemann surface, and show how to construct the moduli theory of polarized abelian varieties.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 300

Добавлена в каталог: 01.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$SL_2$ orbit      165
$SL_2$ orbit theorem      165
$\Delta$-polarized abelian variety      49
Abel — Jacobi mapping      107
Abelian category      112
Abelian variety      41
Abel’s theorem      61
Adjoint representation      32
Affine Grassmannian      274
Albanese variety      60
Algebraic curve      182
Algebraic stack (in the sense of Artin)      273
Analytic family      2
Analytic family of G-bundles      31
Analytic family of G-bundles, parametrized by S      31
Appell — Humbert Theorem      42
Bidifferential      243
Calabi — Yau variety      140
Canonical curve      73
Canonical extension      163
Canonical mapping      76
Canonical prolongation      120 163
Cartan — Killing form, normalized      193
Central charge      198
Classifying space of Hodge structures      124
Clebsch — Gordan coefficient      267
Clemens — Schmid exact sequence      169
Coarse moduli space      93
Cohomological mixed Hodge complex      159
complete      8
Complex analytic family      2
Complex analytic family of G-bundles      31
Complex torus      36
Conformal blocks      207
Conformal blocks, dual      207
Conformal blocks, sheaf of      234
Conformal blocks, sheaf of dual      234
Connected sum      214
Connection flat      115
Connection, Gauss — Manin      117
Connection, integrable      115
Connection, projective      244
Contraction      135
Correlation function      223
Correlation function of currents      225
Correlation function of energy-momentum tensors      225
Critical locus      189
Current      197
Deformation      2
Deformation of a principal G-bundle      31
Discriminant locus      189
Divisor with normal crossings      155
Dominant integral weight      195
Donagi’s theorem      146
Dual conformal block      207
Dualizing sheaf      183
Effective divisor      61
Energy-momentum tensor      197
Factorization theorem      230
Faltings’ theorem      269
Family of stable N-pointed curves of genus g with formal neighbourhoods      186
Family of stable N-ppointed curves of genus g with n-th infinitesimal neighbourhoods      187
Filtered R-module      209
Filtered ring      208
Filtration N-      166
Filtration, Hodge      108
Filtration, limit Hodge      164
Filtration, monodromy weight      166
Filtration, stupid      157
Filtration, weight      150
Flat connection      96
Formal coordinates      185
Formal neighbourhoods      184
Fusion ring (or fusion algebra)      264
Fusion rule      264
Fusion rule, non-degenerate      264
Gabber’s theorem      209
Gauge condition      208
Gauss map      78
Gauss — Manin connection      117
Gauss — Manin connection, regularity of      120
Generic global Torelli problem      137
Genus      182
Graded ring      208
Graded-polarizable      151
Griffiths transversality      118
Hard Lefschetz theorem      110
Highest weight      195
Highest weight vector      111 195
Hironaka’s theorem on resolution of singularities      155
Hirzebruch — Nagata surface      13
Hodge decomposition      103
Hodge filtration      108
Hodge index theorem      115
Hodge structure of Tate type      105
Hodge structure, A-Hodge structure      104
Hodge structure, classifying space of      124
Hodge structure, morphism of A-Hodge structure      112
Hodge structure, polarization      113 121
Hodge structure, Tate Hodge structure      105
Hodge structure, variation of A-Hodge structure      118
Hodge — Riemann bilinear relations      114
Hopf surface      14
Horizontal map      134
Horizontal tangent bundle      133
Horizontal tangent vector space      129 133
Hyperelliptic involution      82
Index of unipotency      162
Infinitesimal deformation      4
Infinitesimal Torelli problem      136 138
Infinitesimal variation of Hodge structure      146
Integrable highest weight representations      195
Integrable symplectic group      46
Intermediate Jacobian variety      106
Isogeny      71
Jacobian variety      60
Kaehler differential      183
Kaehler morphism      115
Knizhnik — Zamolodchikov equation      259
Kodaira — Spencer mapping      5
Kuranishi family      10
Kuranishi space      10
KZ equation      259
Label      207
Lefschetz operator      110
Level      195
Level n-structure      51
Limit Hodge filtration      164
Limit mixed Hodge structure      165
Local invariant cycle theorem      170
Locally liftable map      134
Locally nilpotent      196
Logarithmic differential form      156
Loop Grassmannian      274
Mixed Hodge structure (MHS)      150
Mixed Hodge structure limit      165
Mixed Hodge structure, graded-polarizable      151
Mixed Hodge structure, morphism of      151
Mixed Hodge structure, pure      151
Moderate growth,      120
Monodromy representation      131
Monodromy theorem      162
Monodromy weight filtration      166
Morphism of A-Hodge structure      112
Morphism of mixed A-Hodge structures      151
N-filtration      166
N-th infinitesimal neighbourhoods      184
Nagata’s embedding theorem      155
Newlander — Nirenberg theorem      29
Nilpotent orbit      164
Nilpotent orbit theorem      164
Normal ordering      196
Normalized Cartan — Killing form      193
Obstruction class      21
Orbit $SL_2$      165
Orbit, nilpotent      164
Ordinary double point      182
Paramodular group      46
Perfect pairing      203
Period domain      124
Period domain, compact dual      124
Period mapping      132
Period matrix      36 56
Picard variety      39
Picard — Puchs equation      97
Poincare residue      156
Poisson bracket      209
Polarization      113 121
Polarization of type $(d_1,... ,d_g)$      49
Polarization of type $\Delta$      49
Polarized Abelian variety      49
Polarized abelian variety of type $(d_1,... ,d_g)$      49
Primitive decomposition      111
Primitive part      110
Principal G-bundle      31
Principally polarized abelian variety      49
Projective connection      244
Prym mapping      148
Prym variety      148
Pullback family      2
Pure mixed Hodge structure      151
Quasi-isomorphic      108
Quasi-unipotent      162
Regularity of Gauss — Manin connection      120
Removable singularity theorem      135
Riemann conditions      45 59
Riemann constant      65
Riemann theta function      53
Root vector      193
Satake compactification      52
Schottky problem      96
Schwarzian derivative      217
Semi-character      42
Semi-stable curve      182
Semi-stable degeneration      161
Semi-stable reduction theorem      161
Semi-universal      9
Sheaf of conformal blocks      234
Sheaf of dual conformal blocks      234
Siegel modular group      46
Siegel upper half plane      46
Siegel upper half space      46
Smooth      10
Smooth family      2
Spectral sequence, Hodge-to-de Rham      107
Spectral sequence, Leray      159
Spectral sequence, weight      157
Stable N-pointed curve      182
Stable N-pointed curve with formal neighbourhoods      184
Stable N-pointed curve with n-th infinitesimal neighbourhoods      184
Strictly compatible      112
Stupid filtration      157
Symmetric product      62
Symplectic basis      45
Tate twist      105
Theorem of the fixed part      160
Theta characteristic      54
Theta divisor      63
Theta function, Riemann      53
Torelli      136
Torelli, generic global Torelli problem      137
Torelli, global Torelli problem      137
Torelli, infinitesimal Torelli problem      136 138
Torelli, local Torelli problem      138
Torelli, Torelli’s theorem      78
Torelli, weak global Torelli problem      137
Unipotent      162
Universal      9
Vacua      207
Variation of (A-)Hodge structure (VHS)      118
Variation of (A-)Hodge structure (VHS), infinitesimal      146
Variation of (A-)Hodge structure (VHS), morphism of      121
Variation of (A-)Hodge structure (VHS), polarized      121
Varieties with normal crossings      160
Verlinde formula      261 262
Verlinde isomorphism      271
Versal      9
Virasoro algebra      198
Weak global Torelli problem      137
Weight filtration      150
Weil operator      113
Zariski tangent space      10
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