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| Arbarello E., Harris J., James R. — Geometry of Algebraic Curves (Vol. 1) |
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| Предметный указатель |
 in genus 4 196
, definition of 154
, dimension of 159
, non-emptiness 206
, tangent space to 162 163 197
 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  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,  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  ’s 198
Mumford’s theorem for birational maps 198
Nearly extremal curves 149
Net 4
Net of quadrics in  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  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  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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