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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

Dualizing sheaf, relative      84
Eisenbud, David      245 330
Elliptic tail      54 128
Enriques, F.      62
Equigeneric deformation      94
Equisingular deformation      93
Extrinsic pathologies, double space lines      24
Extrinsic pathologies, Mumford’s example      19
F(Y)      226
Faber, Card      68—70 138
Fan      17
Fibered category      40
Fine moduli space      2 35
Fine moduli space, obstructions to existence of      36
First-order deformation      13
First-order Schiffer variation      91
Fitting ideal      102
Flag curves      247
Flag curves, limit linear series on      274—285
Flag curves, limit linear series on, $\rho$ = 0, with      276
Flag curves, limit linear series on, canonical      276
Flag curves, limit linear series on, inequalities for      274
Flag curves, schematic diagram      247
Flat completion      138
Flat family      6
Flat limit, examples      138
Flexes      134
Formulas, genus      81
Formulas, Grothendieck — Riemann — Roch      154
Formulas, Hirzebruch — Riemann — Roch      154
Formulas, Porteous’      161 (see also “Porteous’ formula”)
Fourfold point      136
Franchetta, A.      62
Fulton, Bill      76 262 268 288
Functor of points      2
G.I.T.      46
G.I.T., alternatives to      238
G.I.T., linearization      195
G.I.T., plane cubics, of      204
G.I.T., plane curves, of      202—206
G.I.T., problem      193
G.I.T., quotient map      194
G.I.T., quotient map, base locus      197
G.I.T., quotient map, fibers      198
G.I.T., simplifying assumptions      193 197
G.I.T., strategy      193
General curves, historical overview of theorems about      241—247
Generalized Severi variety      see “Severi variety generalized”
Genus formula      81
Geometric invariant theory      see “G.I.T.”
Geometrically reductive      196
Gieseker — Petri theorem      240 (see also “Brill — Noether”)
Gieseker — Petri theorem, proof      280—285
Gieseker, David      191 211 215 220 223 240 243 285
Gieseker’s criterion      215
Gieseker’s criterion, application      216—219
Gonality      185
Gorenstein singularity      82
Gotzmann, G.      9
Griffiths, Phil      243
Gromov — Witten invariant      79
Gromov, M.      79
Grothendieck duality      85
Grothendieck group, coherent sheaves, of      151
Grothendieck group, vector bundles, of      151
Grothendieck — Riemann — Roch, applications      154—160
Grothendieck — Riemann — Roch, formula      154
Grothendieck — Riemann — Roch, setup for      151
Grothendieck, Alexandre      6 40 154
Haboush, Bill      195
Halphen, G. H.      24
Harer, John      44 58 60
Harris, Joe      30 66 243 245 304 312 328 330
Hartshorne, Robin      17 23
Hartshorne’s Connectedness, theorem      17
Hilbert function      17
Hilbert functor, representability      6
Hilbert number      26
Hilbert point, smooth curve, of a stability      216
Hilbert polynomial      6
Hilbert polynomial, characterization of      18
Hilbert scheme      5 6
Hilbert scheme, cohomology of      64
Hilbert scheme, cohomology of nonstandard classes      64 65
Hilbert scheme, cohomology of standard classes      64
Hilbert scheme, complete subvarieties of      57
Hilbert scheme, connectedness of      17
Hilbert scheme, construction of      5—9
Hilbert scheme, curves      26
Hilbert scheme, dimension      26
Hilbert scheme, dimension at nonspedal curve      27
Hilbert scheme, dimension inequality      26
Hilbert scheme, dimension, open questions      28
Hilbert scheme, divisor classes on      166
Hilbert scheme, equations of      8
Hilbert scheme, examples, elliptic normal curves      14
Hilbert scheme, examples, lines in $\mathbb{P}^3$       9
Hilbert scheme, examples, plane curves      9
Hilbert scheme, examples, rational normal curves      14
Hilbert scheme, examples, twisted cubics      14 15 58
Hilbert scheme, exceptional component      27
Hilbert scheme, general component      27
Hilbert scheme, Murphy’s Law of      18
Hilbert scheme, relative      11
Hilbert scheme, restricted      17
Hilbert scheme, tangent space      12—14
Hilbert scheme, variants, bundles, of      11
Hilbert scheme, variants, maps, of      11
Hilbert scheme, variants, relative      11
Hilbert scheme, variants, subschemes, of      11
Hilbert stable      210
Hilbert — Mumford numerical criterion      see “Numerical criterion”
Hirzebruch — Riemann — Roch, formula      154
Hodge bundle      61 155
Hodge bundle, Chern classes      155—158
Hodge bundle, Chern classes, over $\bar{\mathcal{M}}_g$       158
Hodge bundle, Chern classes, over $\mathcal{M}_g$       156
Hubert, David      195 196 201
Hurwitz scheme      32 52 175
Hurwitz scheme, cohomology of standard classes      65
Hurwitz scheme, rational Heard group      302
Hurwitz, A.      34
Hyperelliptic curve      53 134
Hyperelliptic curve, characterizations of      162
Hyperelliptic curve, universal family of      39
Hyperelliptic locus      293—303
Hyperelliptic locus in $\mathcal{M}_g$ , rational Picard group      302
Hyperelliptic locus, class in $H^{\ast}(\mathcal{M}_g)$       68
Hyperelliptic locus, class in $Pic(\bar{\mathcal{M}}_3\otimes\mathbb{Q})$       188
Hyperelliptic locus, class in $Pic(\mathcal{M}_3\otimes\mathbb{Q})$       164
Hyperelliptic locus, closure of in $\bar{\mathcal{M}}_g$       185
Hyperelliptic locus, general curve in      295
Hyperelliptic locus, general curve in, degree of Hodge bundle      300
Hyperelliptic locus, general curve in, degrees of boundary classes      297
Hyperelliptic locus, general curve in, relative dualizing sheaf      299
Hyperelliptic locus, in $\bar{\mathcal{M}}_g$ , rational Picard group      302
Hyperelliptic locus, inequalities for $\lambda$ and $\delta$ on      294 301
Hyperelliptic locus, Picard group      303
Hyperelliptic locus, rational Heard group, relations to $Pic(\bar{\mathcal{M}}_g$       303
Hyperelliptic locus, smoothness of $\mathcal{M}_g$ along      53
Hyperelliptic locus, universal family over      39
Hyperelliptic stable curve      169
Hyperflex      189
Hyperstall      167
Inflection point      see “Ramification point”
Invariants, finite generation of      195
Invariants, separation by      196
Jacobian bundle      41
Jacobian ideal      97
Jacobian of a nodal curve      249

k-gonal      185
Karu, Kalle      150 238
Kempf, George      241 262
Kleiman, Steve      241 243 262
Klein, Felix      34
Knudsen, Finn      177 223
Kodaira — Serre duality      83
Kodaira — Spencer map      106
Kodaira — Spencer map at a point      107
Kodaira — Spencer map, global      107
Kodaira, Kunihiko      56 87 106
Kodaira’s construction      56
Kollar, Janos      10 87 142 238 329
Kontsevich, Maxim      44 71 76
Korteweg-deVries      74
Kouvidakis, Alexis      310
Kuranishi      87
Kuranishi family      87
Laksov, Dan      241 262
Lang, Serge      343
Lazarsfeld, Rob      247 262
Lefshetz, Solomon      97
Level n structure      38
Level structures      37
Lexicographical ideal      8
Liaison formula      21
Limit linear series      263 253—272
Limit linear series, aspects      255
Limit linear series, aspects, relations amongst      255
Limit linear series, canonical      269—272
Limit linear series, dimensionally proper      264
Limit linear series, flag curves, on      274—285
Limit linear series, flag curves, on, $\rho$ = 0, with      276
Limit linear series, flag curves, on, canonical      276
Limit linear series, flag curves, on, inequalities for      274
Limit linear series, refined      263
Limit linear series, simplest example      253
Limit linear series, smoothing      266
Limit linear series, smoothing of      268
Line bundle, limits of      251—252
Line bundle, Poincare      63
Line bundle, stable curve, on a      247—251
Looijenga, E.      68
Luroth, J.      34
Macaulay, F. S.      17
Marked point      37
Mestrano, Nicole      62 63
Miller, Ed      60
Modular      4
Moduli functor      2
Moduli problem      1
Moduli problem, rigidified      37
Moduli space      see “ $\mathcal{M}_g$
Moduli space, elementary examples, j-line      4 36
Moduli space, elementary examples, lines in       4
Moduli space, elementary examples, plane conies      4
Moduli space, versus parameter space      5
Moduli stable      47
Moduli stack      see “Stack moduli”
Moishezon, Boris      34
Monodromy of branched covers      33 52 176 292
Monodromy of cubic surfaces      19
Monodromy of nodes of plane curves      314
Monodromy of subcanonical line bundles      63
Monomial basis      208
Mordell, L      343
Morrison, Ian      211 330
Mumford, David      6 18 40 48 60 68 191 198 201 328 332
Mumford’s example      19
Nagata, M.      195 196
Nodal curve, genus formula      81
Nodal reduction      119
Node, general      310
Node, special      310
Noether, Max      97 242
Nonsemistable      197
Normal sheaf      96
Numerical criterion, asymptotic      210
Numerical criterion, general statement      201
Numerical criterion, Hilbert points, for      208
Numerical criterion, plane curves, for      203
Openness of nodality      102
Openness of versality      105 144
P      6
Palamodov, V.      87
Pandharipande, Rahul      76
Parameter space, versus moduli space      5
Pathologies      19
Period matrix      44
Petri divisors      332
Petri, K.      240 285
Picard variety of a nodal curve      249
Piene, Ragne      15
Pigtail      122 175
Planar singularity      98
Poincare line bundle      63
Pointed stable curve      47
Popp, H.      142
Porteous, I. R      161
Porteous’ formula      161
Porteous’ formula, applications      162—168
Potential stability theorem      225
Potential stability theorem, first basic estimate      228
Potential stability theorem, second basic estimate      228
Potentially stable      224
Potentially stable curve      224
Pseudo-admissible covers      186
Quantum cohomology ring      79
Quotient map      194
Quotient map, base locus      197
Quotient map, fibers      198
Ramanan, S.      63
Ramification index      257
Ramification index, Plucker formula for      257
Ramification point      167
Ramification sequence      256
Ramification sequence, basic inequality for      260
Ran, Ziv      57 329
Rational action      195
Rational divisor class on $\bar{\mathcal{M}}_g$       140
Rational divisor class on a moduli stack      140—148
Rational divisor class, associated to $\Delta$       145—147
Rational divisor class, associated to a hypersurface in $\bar{\mathcal{M}}_g$       144
Rational normal scroll      25
Rational numerical polynomial      18
Regeneration theorem      268
Relative cotangent bundle of $\bar{\matcal{C}}_g$ , over $\bar{\mathcal{M}}_g$ , Todd class      158
Relative cotangent bundle of y over B, Chern character      158
Relative dualizing sheaf      59 60 62 64 68 84 102 155
Relative dualizing sheaf, ampleness      309
Relative dualizing sheaf, hyperelliptic curves      298
Representable functor      2
Restricted Hubert scheme      17
Reynolds operator      195
ribbon      24
Riemann — Roch formula      150
Rigid curves      29
Rigidifying      37
Rigidifying, $R^{\ast}(\mathcal{M}_g)$       67
Rigidifying, $R^{\ast}(\mathcal{M}_g)$ , Looijenga’s theorem for      68
Rigidifying, approaches, level structures      37
Rigidifying, approaches, marked points      37
Rigidifying, approaches, Weierstrass points      38
Satake compactification      45
Satake, I.      45
Schiffer variation      91
Schiffer variation, first-order      91
Schiffer variation, versality of      92
Schlessinger, Michael      15
Schreyer, Frank-Olaf      329

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