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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

!      154
      256
singularity      118
      256
      161
      211
      226
$D_{=n}$       125
      210
      211
$Hilb_{P,r}$       6
$Hilb_{P,r}$ , representability      6
      162
, in terms of standard classes      162—164
, rational Picard group      302
      226
$h_{d,g,r}$       26
      165
      151
      151
      226
$K_{Y,Z}$       226
$K_{\bar{\mathcal{M}}_f}$ in terms of standard classes      160
$M_{a,b}$       161
      6
      55
      226
$S{\lambda}(W)$       200
$S{\lambda}(\chi)$       200
      99
, stalk at a node      101
$T_{\bar{\mathcal{M}}_g}$ , Chern class of      159
      255
$V_{d,g}$ , irreducibility      30
$V_{d,g}$ , irreducibility, proof      313—328
$V_{d,g}$ , irreducibility, via contracting, degenerations      319
$V_{d,g}$ , irreducibility, via Diaz’ theorem      316
$V_{d,g}$ , irreducibility, via general degenerations      314
, tangent space to      95
      208
      208
$\alpha_F$       210
$\bar{H}_g$       168
$\bar{H}_g$ , $\bar{H}_3$ in terms of standard classes      168—172
$\bar{H}_g$ , inequalities for $\lambda$ and $\delta$ on      294 301
$\bar{H}_g$ , Picard group      303
$\bar{H}_r$       168
$\bar{\mathcal{H}}_{d,g}$       175
$\bar{\mathcal{H}}_{d,g}$ , desired properties      175
$\bar{\mathcal{H}}_{d,g}$ , existence theorem for      181
$\bar{\mathcal{M}}_g$       48
$\bar{\mathcal{M}}_g$ , ample cone      312
$\bar{\mathcal{M}}_g$ , canonical class      160
$\bar{\mathcal{M}}_g$ , construction      220—223
$\bar{\mathcal{M}}_g$ , construction, consequences      223—224
$\bar{\mathcal{M}}_g$ , construction, plan      220
$\bar{\mathcal{M}}_g$ , cotangent bundle, Chern character      159
$\bar{\mathcal{M}}_g$ , divisor classes, relation to classes on $Pic_{fun}(\bar{\mathcal{M}}_g)$       144
$\bar{\mathcal{M}}_g$ , divisor classes, relations on      145
$\bar{\mathcal{M}}_g$ , irreducibility of      223
$\bar{\mathcal{M}}_g$ , Kodaira dimension, $g \geq$       22 329
$\bar{\mathcal{M}}_g$ , Kodaira dimension, $g \leq$       23 328
$\bar{\mathcal{M}}_g$ , Kodaira dimension, basic criterion      330
$\bar{\mathcal{M}}_g$ , local description of      223
$\bar{\mathcal{M}}_g$ , local structure      53
$\bar{\mathcal{M}}_g$ , projectivity of      223
$\bar{\mathcal{M}}_g$ , rational points on      342
$\bar{\mathcal{M}}_g$ , relations on divisors disjoint, from subloci      336—341
$\bar{\mathcal{M}}_g$ , singular locus      54
$\bar{\mathcal{M}}_g$ , slope conjecture      333
$\bar{\mathcal{M}}_g$ , tangent bundle, Chern class of      159
$\bar{\mathcal{M}}_{g,n}(X,\gamma)$       76
$\bar{\mathcal{M}}_{g,n}(X,\gamma)$ , properties of, for convex X      77
$\bar{\mathcal{P}}_{d,g}$       49
$\beta(i,V)p$       257
$\beta(V, p)$       257
$\b_i(V,p)$       256
$\Delta$       50
$\Delta$ , infinitesimal description in $\bar{\mathcal{M}}_g$       101
$\Delta$ , normal bundle to in $\bar{\mathcal{M}}_g$       101
$\Delta$ , rational divisor class associated to      145—147
$\Delta_0$       50
$\Delta_0$ , irreducibility of      54
$\Delta_i$       50
$\Delta_i$ , irreducibility of      54
$\Delta_{a,b}$       161
$\eta$       60
$\Gamma_g$       43
$\kappa_1$       60
$\kappa_i$       60
$\lambda$       61
$\lambda$ -state, representation, of a      200
$\lambda$ -state, vector, of a      200
$\lambda$ -weight, representation, of a      200
$\lambda$ -weight, space      200
$\lambda$ -weight, vector, of a      200
$\lambda_i$       61
$\mathbb{I}$       12
$\mathbb{I}_k$       12
$\mathbb{I}_k^{(l)}$       12
$\mathcal{A}_g$       44
$\mathcal{C}_G$       41
$\mathcal{C}_g$ , cohomology of      62
$\mathcal{C}_g$ , Picard group of      62
$\mathcal{C}_g^d$       69
$\mathcal{G}_d^r$       267
$\mathcal{H}_{d,g,r}$       16
$\mathcal{H}_{P,r}$       6
$\mathcal{J}_k^m$       166
$\mathcal{K}$       46
$\mathcal{L}_Y$       226
$\mathcal{M}^0$       37
$\mathcal{M}_1$       202
$\mathcal{M}_g$       37 46
$\mathcal{M}_g$ , cohomology of      58
$\mathcal{M}_g$ , dimension      52
$\mathcal{M}_g$ , functions on      45
$\mathcal{M}_g$ , irreducibility      52 286
$\mathcal{M}_g$ , local structure      52
$\mathcal{M}_g$ , singular locus      53
$\mathcal{M}_g$ , stratifications, Arbarello’s      289
$\mathcal{M}_g$ , stratifications, Diaz’      291 292
$\mathcal{M}_g$ , topology of      43
$\mathcal{M}_g$ , universal curve over      41
$\mathcal{M}_{0,3d}(\mathbb{P}^2, d)$       78
$\mathcal{M}_{0,3d}(\mathbb{P}^2, d)$ , enumerative applications      78—79
$\mathcal{M}_{g,n}$       41
$\mathcal{P}_{d,g}$       41 49
$\mathcal{R}$       17
$\mathcal{T}_g$       43
$\mu(\chi)$       200
$\rho$       27 240
$\tilde{r}_g$       57
$\tilde{\mathcal{A}}_g$       45
$\tilde{\mathcal{K}}$       46
$\tilde{\mathcal{K}}_{ss}$       221
$\tilde{\mathcal{K}}_{ss}$ , properties, claims      221
$\tilde{\mathcal{K}}_{ss}$ , properties, verifications      234—237
$\varepsilon_c$       215
$\varepsilon_j$       215
Abramovich, Dan      150
Adjunction conditions      332
Adjusted Brill — Noether number      264
Adjusted Brill — Noether number, additivity      264
Adjusted Brill — Noether number, estimates for      264
Admissible covers      34 180
Admissible covers, applications      286
Admissible covers, existence theorem for      181
Admissible covers, properties      177—184
Admissible covers, pseudo-      186

Admissible covers, simplest cases      178
Admissible covers, topological description      179
Admissible covers, two branch points meet, admissible description      181
Admissible covers, two branch points meet, naive description      176
Algebraic space      39
Algebraic stack      see “Stack algebraic”
Aluffi, Paolo      138
Arbarello, Enrico      62 288 329
Artin, Michael      39 89
Aspects, limit linear series      255
Aspects, relations amongst      255
Asymptotic numerical criterion      210
B-monomial basis      208
Baily — Borel compactification      45
Base change      124
Base change, prime order, of effect on special fibers      125
Bayer, Dave      8
Bitangent      134 167
Boundary in $\bar{\mathcal{M}}_g$       50 (see also “ $\delta$
Boundary, codimension      45 50
Brill — Noether number      27 161 240
Brill — Noether number, adjusted      264
Brill — Noether number, adjusted, estimates for      264
Brill — Noether, divisor on $\bar{\mathcal{M}}_g$       332
Brill — Noether, divisor on $\bar{\mathcal{M}}_g$ , pullbacks to $\bar{\mathcal{M}}_{0,g}$ and $\bar{\mathcal{M}}_{2,1}$       335
Brill — Noether, divisor on $\bar{\mathcal{M}}_g$ , standard classes, in terms of      332
Brill — Noether, first proof      261
Brill — Noether, flag curves, via      246
Brill — Noether, generalized      265
Brill — Noether, generalized, converse of      268
Brill — Noether, Gieseker’s approach      243
Brill — Noether, Griffiths — Harris’s argument      243
Brill — Noether, Lazarsfeld’s approach      247
Brill — Noether, ray theorem      332
Brill — Noether, second proof      265
Brill — Noether, Seven’s argument      242—243
Brill — Noether, third proof      275
Brill, A.      242
Burnol, Jean-Francois      52
c()      152
Canonical class of the moduli stack      159
Caporaso, Lucia      49 225
Castelnuovo curves      25
Castelnuovo, Guido      242
ch()      152
Chang, Mei-Chu      57 329
Chern character      152
Chern character, alternate characterization      153
Chern character, expansion formula      152
Chern character, properties      153
Chern polynomial      161
Chow variety      10
Ciliberto, Ciro      66
Clebsch, A.      34
Coarse moduli space      3
Coarse moduli space, uniqueness of      4
Compact type      250
Complete deformation      87
Conjectures, Enriques-Franchetta      62
Conjectures, Faber’s on $R^{\ast}(\matcal{M}_g)$       68—70
Conjectures, Kodaira dimension of moduli      329
Conjectures, Lang      343
Conjectures, rigid curves      29
Conjectures, Severi      see “Severi variety irreducibility”
Conjectures, slope conjecture      333
Conjectures, standard      59 60
Conjectures, Witten’s, KdV form      74
Conjectures, Witten’s, Lie form      75
Convex variety      77
Cornalba, Maurizio      62 304 312 329
Cukierman, Fernando      342
Curves, Castelnuovo      25
Curves, compact type      250
Curves, defined over $\mathbb{Q}$       342—343
Curves, degree 2      4
Curves, elliptic normal      14
Curves, genus 1      4 14 36 38
Curves, genus 2      39 53 175 328
Curves, genus 23      279
Curves, genus 3      39 53 57 133—138 162—164 168—175 186—190 245 328
Curves, genus 4      164 190 276 328
Curves, genus 5      189 276 328
Curves, genus 6      276 328
Curves, genus 7      329
Curves, Mumford’s example      19—23
Curves, plane cubics      202—204
Curves, plane quartics      57 133—138 164 170 206
Curves, plane quartics, bitangents to      134
Curves, plane quartics, flexes      135
Curves, plane sextics      135
Curves, potentially stable      224
Curves, rational normal      14
Curves, rigid      29
Curves, space, complete families      57
Curves, space, degree 5      10
Curves, space, degree 6      10
Curves, symmetric product, tangent space to      94
Curves, treelike      265
Curves, twisted cubics      10 14 58
Curves, universal      41
Cusp      98 121—130 204 206 232 318
Deformation      87
Deformation, complete      87
Deformation, curve with line bundle, of a      93
Deformation, curve, of a      92
Deformation, equigeneric      94
Deformation, equisingular      93
Deformation, equivalence of      87
Deformation, first-order      87
Deformation, first-order, curve with effective divisor, of a      94
Deformation, first-order, curve with line bundle, of a      96
Deformation, first-order, cusp      98
Deformation, first-order, line bundle over a fixed curve, of a      95
Deformation, first-order, local complete intersection, of a      99
Deformation, first-order, map with fixed source and target, of a      96
Deformation, first-order, map with fixed target, of a      96
Deformation, first-order, nodal curve      100
Deformation, first-order, node      98
Deformation, first-order, ordinary triple point      98
Deformation, first-order, planar curve singularity      97
Deformation, first-order, pointed curve, of a      94
Deformation, first-order, Schiffer variation      91
Deformation, first-order, singular variety, of a      99
Deformation, first-order, smooth curve      89
Deformation, first-order, tacnode      98
Deformation, map with fixed source and target, of a      93
Deformation, map with fixed target, of a      93
Deformation, map with tangency conditions, of a      111—117
Deformation, map, of a      105—111
Deformation, minimal      88
Deformation, n-th-order      87
Deformation, pointed curve, of a      92
Deformation, Schiffer variation      91
Deformation, three step paradigm      88
Deformation, universal      88
Deformation, versal      87
Degree inequality, general family, for a      305
Degree inequality, singular family, for a      311
Deligne — Mumford stable      47
Deligne, Pierre      48
Diaz, Steve      57 66 292 342
Dilaton equation      72
Dimension inequality      26
Dimensionally proper      264
Divisor, reduced mod n      125
Dolgachev, Igor      329
Double line      15 24 77
Dual graph      249
Dualizing sheaf      82
Dualizing sheaf, ampleness of      83

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