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Harris J., Morrison I — Moduli of curves

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Название: Moduli of curves

Авторы: Harris J., Morrison I

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 369

Добавлена в каталог: 12.03.2005

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Предметный указатель

Semistable      47 48 197
Semistable reduction      51 118
Semistable, characterization by invariants      198
Sernesi, Edoardo      329
Serre, Jean-Pierre      8
Seshadri, C      223
Severi conjecture      see “Severi variety irreducibility”
Severi variety      11 30 52 108
Severi variety, cohomology of standard classes      65
Severi variety, density of nodal curves      30 110
Severi variety, dimension      30 110
Severi variety, dimension estimate      108
Severi variety, generalized      113
Severi variety, generalized, dimension estimates      114 117
Severi variety, generalized, local description      114
Severi variety, irreducibility      30
Severi variety, open problems      31
Severi, F.      30 242 314
Sheaves, normal      96
Shepherd-Barron, Nick      329
Shriek operator      154
Siegel upper halfspace      44
Singularity, Gorenstein      82
Singularity, planar      98
Singularity, terminal      332
Slope conjecture      333
Spencer, D.      106
Stability theorem      58
Stable      197
Stable cohomology ring      59
Stable curve      47
Stable curve, compact type      250
Stable curve, Deligne — Mumford      47
Stable curve, divisors, Abel — Jacobi theorem for      251
Stable curve, divisors, linear equivalence of      251
Stable curve, families, ampleness of relative to      309
Stable curve, families, basic inequality for standard classes      309
Stable curve, families, line bundles on      251—252
Stable curve, genus formula      81
Stable curve, line bundles on      247—251
Stable curve, moduli      47
Stable curve, pointed      47
Stable hyperelliptic curve      185
Stable limit      51
Stable map      76
Stable map, genus g with n marked points of      76
Stable map, moduli space of      76
Stable reduction      118
Stable reduction over general bases      150
Stable reduction, examples      120—138
Stable reduction, examples, glueing transverse sections      120
Stable reduction, examples, smoothing of cusp      122
Stable reduction, examples, smoothing of double conic      133
Stable reduction, examples, smoothing of double cubic      135
Stable reduction, examples, smoothing of quadruple point      136
Stable reduction, examples, smoothing of triple conic      135
Stable reduction, examples, smoothing of triple point      131
Stable reduction, practical considerations      124
Stable, characterization by invariants      198
Stable, Hilbert      210
Stably equivalent      185
Stack, algebraic      40
Stack, moduli      139
Stack, moduli, canonical class of      159
Stack, moduli, rational divisor class on      140—148
STALL      167
Standard, cohomology classes      59
Standard, cohomology classes, relations amongst      165
Standard, cohomology subring      60
Standard, conjectures      59 60
State      200
Stratifications, Arbarello’s      289
Stratifications, Diaz’      291 292
Strictly semistable points      198
String equation      72
Subcanonical point      164
Symmetric product, tangent space to      94
Symplectic basis      37
Tacnode      82 98 232 326—327
Tangent spaces, Hilbert scheme      14
Tangent vectors, addition of      12
Tautological classes      59
Tautological families      142 148
td()      153
Teichmuller space      43
Terminal singularity      332
Test curves      170
Test curves, contained in $\Delta$       172—175 186—188
Theorems, additivity of adjusted, Brill — Noether number      264 _
Theorems, ample cone of $\bar{\mathcal{M}}_g$       312
Theorems, ampleness of relative $\omega$       309
Theorems, aspects, nonvanishing sections      260
Theorems, aspects, relations between       261
Theorems, aspects, special bases      260
Theorems, asymptotic numerical criterion      210
Theorems, basic properties of $\tilde{\mathcal{K}}_{ss}$       221
Theorems, basic ramification/vanishing sequence      260
Theorems, Bers      43
Theorems, Brill — Noether      240
Theorems, Brill — Noether ray      332
Theorems, Brill — Noether, converse of      268
Theorems, Brill — Noether, first proof      261
Theorems, Brill — Noether, flag curves, via      246
Theorems, Brill — Noether, generalized      265
Theorems, Brill — Noether, Gieseker’s approach      243
Theorems, Brill — Noether, Griffiths-Harris’s argument      243

Theorems, Brill — Noether, Lazarsfeld’s approach      247
Theorems, Brill — Noether, second proof      265
Theorems, Brill — Noether, Severi’s argument      242—243
Theorems, Brill — Noether, third proof      275
Theorems, Chang — Ran      57
Theorems, characterization of k-gonality      185
Theorems, comparing divisor class, relations in families and on $\bar{\mathcal{M}}_g$       145
Theorems, connectedness of $\tilde{\mathcal{H}}_{d,g}$       34
Theorems, Cornalba — Harris inequality      304
Theorems, degree inequality, general stable families      305
Theorems, degree inequality, hyperelliptic families      301
Theorems, Diaz’      57 288—293
Theorems, dimension estimate for $V^{\beta}_{d,g}$       117
Theorems, dimension of the Severi variety      110
Theorems, divisors on $\bar{\mathcal{M}}_g$ disjoint from certain loci      334
Theorems, equations defining the $Hilb_{P,r}$       8
Theorems, existence of $\bar{\mathcal{H}}_{d,g}$       181
Theorems, existence of $\bar{\mathcal{M}}_g$       48 222
Theorems, existence of complete, subvarieties of $\mathcal{M}_g$       56
Theorems, Gieseker — Petri      240 (see also “Brill — Noether”)
Theorems, Gieseker — Petri, proof      280—285
Theorems, Gieseker’s criterion      215
Theorems, Grothendieck — Riemann — Roch      154
Theorems, Grothendieck’s      6
Theorems, Harer’s      58
Theorems, Harer’s stability      58
Theorems, Harris — Mumford      328 (see also “ $\bar{\mathcal{M}}_g$ Kodaira
Theorems, Harris’      see “Severi variety irreducibility”
Theorems, Hartshorne’s      17
Theorems, Hilbert — Mumford numerical criterion      201
Theorems, Hilbert — Nagata      196
Theorems, Hilbert — Weyl — Haboush      195
Theorems, Hurwitz’      33
Theorems, innnitesimal description of $\Delta \subset \bar{\mathcal{M}}_g$       101
Theorems, irreducibility of $\bar{\mathcal{M}}_g$       223_
Theorems, isomorphism $Pic_{fun}(\bar{\mathcal{M}}_g)\oimes\mathbb{Q}$ and $\bar{\mathcal{M}}_g\oimes\mathbb{Q}$       141
Theorems, Kontsevich’, KdV form      74
Theorems, Kontsevich’, Lie form      75
Theorems, Kouvidakis’      42
Theorems, limits of canonical series      277
Theorems, local description of $V^{\beta}_{d,g}      114
Theorems, Looijenga’s theorem on $R^{\ast}(\mathcal{M}_g)$       68
Theorems, Macaulay’s      18
Theorems, multiplicity in $Pic_{fun}(\bar{\mathcal{M}}_g)$ of classes in $Pic(\bar{\mathcal{M}}_g)$       144
Theorems, nodal reduction      119
Theorems, Noether — Lefschetz      97
Theorems, numerical criterion for Hilbert points      209
Theorems, open Diaz strata      292
Theorems, openness of nodality      102
Theorems, Plucker formula      257
Theorems, potential stability theorem      225
Theorems, projectivity of $\bar{\mathcal{M}}_g$       223
Theorems, reducedness of automorphisms of a stable curve      86
Theorems, regeneration      268
Theorems, relation of $[\Delta_i]$ to $\delta_i$       147
Theorems, Reynolds lemma      196
Theorems, semistable reduction      118
Theorems, smoothness of $\tilde{\mathcal{K}}$       103
Theorems, stability of smooth curves of large degree      216
Theorems, stable reduction      118
Theorems, stable reduction over general bases      150
Theorems, subloci disjoint from, Brill — Noether divisors      335
Theorems, tautological families over $\bar{\mathcal{M}}_g$       142
Theorems, theta characteristics      134 190 342
Theorems, Uniform m lemma      7
Theorems, Weierstrass points, existence of      273
Theorems, Weierstrass points, limits of      271
Todd class      153
Todd class, expansion formula      153
Todd class, multiplicativity      154
Torsion-free sheaves      243
Total Chern class      152
Treelike curves      265
Trigonal      185 189
Triple point      82 98 131—132 232
Uniform position principle      314
Uniform to lemma      7
Universal, curve      41
Universal, curve, relative Todd class over $\bar{\mathcal{M}}_g$       158
Universal, family      2 38
Vanishing sequence      256
Vanishing sequence, basic inequalities for      260
Versality      87
Viehweg, Eckhard      6 238
Virasoro algebra      75
Vistoli, Angelo      87 89
Weierstrass points      38 135 164 187 189
Weierstrass points, class of      342
Weierstrass points, existence of      273
Weierstrass points, gap sequence      272
Weierstrass points, limits of      271
Weierstrass points, proper      272
Weierstrass points, semigroup      272
Weierstrass stratification      272
Weight      200
Weighted basis      207
Weighted basis, compatible with weighted, filtration      208
Weighted filtration      208
Weighted filtration, induced by a surjection      208
Weighted filtration, normalized      216
Weyl, Hermann      195
Whitney product formula      152
Witten, Ed      71 76 79
Y      106
Zagier, Don      70
Zariski, Oscar      30 94

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