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Arbarello E., Harris J., James R. — Geometry of Algebraic Curves (Vol. 1)
Arbarello E., Harris J., James R. — Geometry of Algebraic Curves (Vol. 1)



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Название: Geometry of Algebraic Curves (Vol. 1)

Авторы: Arbarello E., Harris J., James R.

Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 386

Добавлена в каталог: 22.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C_d^r$ in genus 4      196
$C_d^r$, definition of      154
$C_d^r$, dimension of      159
$C_d^r$, non-emptiness      206
$C_d^r$, tangent space to      162 163 197
$G^r_d$      153 177 187 188
Abelian differentials      7
Abelian sums      17
Abelian variety      21
Abel’s theorem      18
Accola’s theorem      275
Adjoint conditions      58
Adjoint divisor      57
Adjoint ideal      57
Adjunction formula in the plane      53
Adjunction formula on a general surface      138
Ample vector bundle      305
Andreotti — Mayer theorem      253
Associated map      37
Automorphisms      44
Base locus      5
Base-point-free, linear series      5
Base-point-free, pencil trick      126
Bi-elliptic curves      198 210 269 276 280
Bi-elliptic curves of genus 5      272
Bi-elliptic curves of genus 6      218
Bi-elliptic curves, embeddings of      221
Brill — Noether matrix      154 159
Brill — Noether number      159 205
Canonical curve      12 117—118
Canonical curve, line bundle      7
Canonical curve, map      10 15
Castelnuouvo’s bound      116
Castelnuouvo’s lemmas      120 151
Castelnuouvo’s number      116
Castelnuouvo’s theorem      151
Castelnuouvo’s theorem on k-normality      141
Chem character      331
Chem classes in G(2, 4)      104
Chem classes of a symmetric product      336
Chem classes of a tensor product      89
Chem classes of kernel bundles      105
Chem polynomial      85
Clifford’s theorem      107
Clifford’s theorem, refinements of      137
Complete interjections      138
Complete linear series      4
Completeness of the adjoint series      54 56 60
Complex torus      20
Connectedness theorem of Fulton — Hansen      271 326
Connectedness theorem of Fulton — Hansen for $W^r_d(C)$      212 314
Connectedness theorem of Fulton — Hansen for degeneracy loci      311
Constructible sheaf      313
Cubic threefold      302
Curve      1
Curves of genus 2      33 40 46 48 278
Curves of genus 3      35 40 46 248 279 303
Curves of genus 4      34 40 47 196 206 276 279
Curves of genus 5      206 270 279 300
Curves of genus 6      209 218 279
De Jonquieres’ formula      359
Deck transformation      47 281
Degeneracy locus      83
Degeneracy locus, connectedness theorem      311
Degeneracy locus, existence theorem      307
Degree of a divisor      2
Degree of a line bundle      7
Degree of a map      9
Determinantal varieties      67 83
Diagonal mappings      358
Difference map      223 262 276
Dimension Theorem      214
Divisor      2
Duality theorem      7
Effective divisor      3
Embedding of degree g + 3      40
Embedding theorem      216
Embedding, criteria for      40
Enriques — Babbage theorem      124
Euler exact sequence      321
Exceptional divisor      9 63 205
Excess linear series      329
Existence theorem      206 311
Extremal curves      117 147 263
Families of curves      288
Families of line bundles      169
Families of linear systems      182
Families of theta characteristics      288
Fermat curve      44
First fundamental theorem of invariant theory      77
First-order deformation of a line bundle      169
First-order deformation of a linear series      185
Fitting ideal      179
Fundamental theorems of invariant theory      71 77
Galois covering      47
Galois extension      281
Gap sequence      41
General position theorem      109
Generic determinantal variety      67
Genus      1
Genus formula for plane curves      53 58 60
Genus of space curves      143
Genus, Castelnuovo’s bound on      116
Gherardelli’s theorem      147
Gieseker’s lemma      145
Gorenstein relation      59
Grothendieck, decomposition      145
Grothendieck, group      85 331
Grothendieck, Riemann — Roch formula      333
Heat equation      24 250
Hodge theorem for curves      54
Hurwitz formula      see “Riemann — Hurwitz formula”
Hyperelliptic curve      10 41 43
Hyperelliptic curve in genus 6      218
Hyperelliptic curve, $W_2(C)$      279
Hyperelliptic curve, embeddings of      221
Hyperelliptic curve, Prym varieties of      303
Hyperelliptic curve, theta-characteristics on      287—292
Hyperelliptic curve, Torelli theorem for      247 269
Ideal of initial forms      62
Index of speciality      8
Inflectionary point      37
Isogeny      49
Jacobi inversion theorem      19 27
Jacobian variety      17
k-normal      140 141
Keem’s theorems      200
Kempf’s singularity theorem      241
Klein canonical curve      123
Kodaira — Spencer class      171
Koszul complex      139
Laurent tail      14
Lefschetz hyperplane theorem      306 315
Linear equivalence      4
Linear series      4
Linear system      4
Linearly normal      140
MacDonald’s formula      350
Martens’ theorem      191
Martens’ theorem for birational maps      198
Mittag — Leffler problem      14
Mittag — Leffler sequence      13
Moduli space      28
Monodromy group      111
Multiplicity of a divisor      2
Multiplicity of a point in a variety      62
Multiplicity of a point on a curve      36
Mumford’s theorem      193
Mumford’s theorem for $g^2_d$’s      198
Mumford’s theorem for birational maps      198
Nearly extremal curves      149
Net      4
Net of quadrics in $\mathbb{P}^4$      270
Newton functions      156
Noether, Max, theorem      117 151
Noether, Max, “AF+BG” theorem      139
Non-degenerate      6
Norm map      281
Normal covering      47
Normal Weierstrass point      42
Normalization      31
Normalized period matrix      22
Order      2
Oscnode      220
Osculating k-plane      37
Pencil      4
Period matrix      16 21
Period matrix, normalized      22
Petri’s construction      127
Petri’s theorem      131
Picard group      18
Plane curves      31
Plane curves, genus formula for      53 59
Plane curves, linear series on      56
Plane quintic curve      see “Quintic plane curve”
Plane sextic curve      see “Sextic plane curve”
Plucker formula      39
Plucker relations      71
Poincare complete reducibility theorem      49
Poincare Formula      25
Poincare line bundle      166
Poincare residue      53
Postulation      56 115 120 142 144 149 199 220
Prill’s problem      268
Principal part of a ineroinorphic differential      14
Principally polarized abelian variety      21
Projections      35 51
Projective bundle      304 317
Projectively normal      140 221
Projectivized tangent cone      62
Prym varieties      297
Push-pull formula      91 318
Push-pull formula for symmetric products      367
Quadrics      102
Quadrics, containing a curve      142
Quadrics, containing a curve in $\mathbb{P}^3$      140
Quadrics, containing a curve of genus 5      270 275
Quadrics, containing a curve, canonical      255
Quadrics, linear spaces on      102
Quadrics, spaces of      100
Quasi-algebraically closed      282
Quintic plane curve      244 264 270—274 300
Ramification, divisor      9
Ramification, index      9
Ramification, sequence, of a map      37
Rational normal curve      6 39
Rational normal scroll      95 121 147
Relative divisor      165
Residual      10
Residue      2
Residue, theorem      3
Riemann surface associated to an algebraic function      31
Riemann — Hurwitz formula      8 39
Riemann — Mumford relation      290
Riemann — Roch theorem      4 7
Riemann — Roch theorem for an abelian variety      21
Riemann — Roch theorem for surfaces      148
Riemann — Roch theorem, geometric version      12
Riemann — Roch theorem, proof via adjoint series      55—56
Riemann, bilinear relations      16 21
Riemann, constant      27
Riemann, inequality      55
Riemann, singularity theorem      226
Riemann, theorem      27
Riemann, theta function      23
Schottky problem      249
Schubert varieties      74
Secant plane      12 152
Secant plane, formula for      340 345
Secant variety      231
Secant variety of a canonical curve      364
Second fundamental theorem of invariant theory      71
Segre class      318
Semicanonical divisors      see “Theta characteristics”
Serre’s criterion      98
Sextic plane curves      209 220 264 275
Sheet number      9
Siegel modular group      23
Siegel upper half plane      22
Simple abelian variety      49
Smoothness theorem      214 215
Special divisor      8
Stable curve      29
Standard monomials      72
Superabundance      56 115 120 142 144 149 199 220
Sylvester’s determinant      87
Symmetric product      18 136 309
Symmetric product, Chern classes of      322 336
Symmetric product, cohomology of      328
Symmetric product, tangent spaces to      171 197
Tangent cone      61
Tangent cone to $W_d^r(C)$      240
Tangent cone to the theta divisor      226 255
Theta characteristics in genus 5      270—274 275
Theta characteristics, definition of      287
Theta divisor      22
Theta divisor, intersection of translates of      267
Theta divisor, singular locus of      250
Theta divisor, tangent cones to      226 255 270
Theta divisor, tangent planes to      268
Theta function      23
Todd class      332
Torelli’s theorem      27 245 263 265 268
Trigonal curves      118 198
Trigonal curves of genus 5      270 279
Trigonal curves of genus 6      218
Trigonal curves, embeddings of      219 221
Trigonal curves, linear series on      138
Uniform position theorem      112
Universal divisor      164
Universal divisor, cohomology class of      336
Universal family of abelian varieties      251
Universal family of curves      29
Veronese map      6
Veronese surface      245
Web      4
Weierstrass, gap sequence      41
Weierstrass, pairs      365
Weierstrass, points      41
Weierstrass, semigroup      41
Weight of a Weierstrass point      42
Weight of a Weierstrass point, connectedness of      212
Weight of a Weierstrass point, definition of      176 177
Weight of a Weierstrass point, dimension of      189 192 193 198 200
Weight of a Weierstrass point, examples of      196 199 206—211 218
Weight of a Weierstrass point, existence of      206
Weight of a Weierstrass point, irreducibility of      214
Weight of a Weierstrass point, multiplicity of      240—241
Weight of a Weierstrass point, tangent spaces to      189 197 269 240
Weil, pairing      284
Weil, reciprocity      283
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