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| Yang K. — Complex Algebraic Geometry: An Introduction to Curves and Surfaces |
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| Предметный указатель |
Abstract algebraic variety 14 15
Abstract coordinate ring 15
Adjunction formula 69
Affine algebraic variety 1
Affine part of a projective variety 3
Algebraic curve 93
Algebraic dimension 164
Algebraic surface 154 157
Ampleness of the canonical divisor 175
Analytic hypersurface 15 17 19
Analytic subvariety 79
Analytic type form 233
Analytic type function 236
Ascending chain condition 4
Associated curves of a projective curve 102 235
Bagnera — de Franchis theorem 191
Base-point-free linear systems 73
Betti numbers 29 80 159
Bezout theorem 25
Birational classification 14 151
Birational equivalence 14 151
Birational map 165
Blow-up 166 168
Boundary map 28
Canonical linear system and divisors 121
Canonical map 147
Cartan matrix 217
Castelnuovo theorem 185
Catelnuovo — Enriques criterion 169
Cech cochain 178
Chain group 29
Chern class 53 61_
Chern connection 228
Chow's theorem 18 87 164 236
class 104
Closed form 32
Closure map 4
Coboundary and coboundary map 31
Cochain group 31
Cocycles 66
Coframe 82
Coherent orientations 27
Complete linear system 174 208
Complex manifold, algebraic/projective 19
Complex manifold, compact 16
Complex manifold, submanifolds 51
Complex manifold, vector bundle 51
Complexified cotangent bundle 48
Conies 93
Connection 55
Connection matrix 55
Connection, metric 57
Coordinate ring 13 96
Curvature form and matrix 56 59
Curve, algebraic 236
Curve, exceptional of the first kind 216
Cusp (simple) 100
Cycles 28
de Rham cohomology groups 32
Dehomogenization of a polynomial 3
Descending chain condition 4
Direct image sheaf 214
Direct system 42
Directed set 42
Divisor 64 68
Divisor, canonical 113
Divisor, integral or effective 112
Divisor, linear equivalence 113
Divisor, principal 65 113
Dolbeault cohomology groups 50 75
Dolbeault isomorphism theorem 50
Dual bundle 54
Dual curve 102
Enriques theorem 183
Euler (topological) characteristic 158
Exact form 32
Extension of line bundles 179
Fixed part of a linear system 174
Flex (ordinary) 100
Frame 55
Frame, Frenet 235 242
Frame, holomorphic 58 81 228
Frame, unitary (metric) 58 82
Fubini — Study metric 90 162 227
Fulton — Hansen theorem 251
Gap (Weierstrass) value 134
Gauss map 102
Gauss-Bonnet theorem 200
Generic subset 24
Genus formula 157
Germs of holomorphic functions 16 52 104
Grassmannian manifolds 221
Grauert theorem 216
Green's operator 39
Hahn — Banach theorem 37
Harmonic form 36
Harmonic type 77
Hermitian structure 57
Hermitian vector bundle 57
Hessian matrix 100
Hilbert analytic Nullstellensatz 154
Hilbert basis theorem 9
Hilbert nullstellensatz 11 17
Hironaka desingularization theorem 166
Hirzebruch — Jung strings 217
Hodge decomposition theorem 80
Hodge star operator 35
Hodge theorm for Hermitian holomorphic vector bundles 82
Holomorphic frame 58 228
Holomorphic implicit mapping theorem 19
Holomorphic section 58
Homogeneous affine variety 2
Homogeneous coordinates 2
Homogeneous ideal 8
Homogeneous representative 101
Homogeneous set 2
Homogenization of a polynomial 3
Homology groups (simplicial) 28 29
Hyperelliptic curve 140
Hyperplane at infinity 2
Hypersurface 21
Hypersurface, analytic 15 17 19
Inhomogenous coordinates 236
Integral (effective) divisor 112
Integrality theorem 224
| Intersection number 25 19 98
Irreducible, affine variety 96
Irreducible, algebraic (affine or projective) variety 10
Irreducible, analytic variety 17 64
Irreducible, curve 184
Irreducible, ideal 10
Jacobian inversion theorem 131
Jacobian map 130
Jacobian variety of a curve 126
Jordan — Holder theorem 21
Kaehler form 60 162 224 229
Kaehler manifold 78
Killing — Cartan form 227
Kodaira dimension 173 175 211
Kodaira embedding theorem 74 160 227
Kodaira vanishing theorem 83
Kodaira — Chow theorem 211
Kodaira — Serre duality 161 200
Kodaira — Spencer theorem 70
Laplace — Beltrami operator 35 236
Lattice (distributive) 5 6
Lefshetz theorem on (1,1) classes 204
Leray theorem 46
Levi's extension theorem 165
Line bundle 63 66
Line bundle, negative and positive 83 156
Linear system 72
Linear system of plane curves 94
Local defining functions 64
Luroth problem 185
Maurer — Cartan form 162 226
Meromorphic function 163
Minimal degree subvarieties 26
Minimal model theorem 186
Mittag — Leffler problem 47
Miyaoka — Yau inequality 211
Model 15
Model, nonsigular 100
Moduli 180 203
Nerve of an abstract simplicial complex 44
Noether — Enriques theorem 176 187 188
Noether's formula 159
Noetherian ring 9
Nondegenerate map 101
Normal bundle 69
Normal form 252
Ordinary m-ple point 105
Osculating map and sequence 236 239 240 241
Osculating metric (singular) 236
Partially ordered set 4
Partition of unity 46
Period map and matrix 123 126
Picard group 113 181
Picard lattice 204
Picard number 204
Plucker embedding 229 234
Plucker formulae for plane curves 106
Plucker formulae for space curves 237
Poincare duality 30 152 156 200
Poincare duality, dual 34 48 69 85 249
Polar class 261
Presheaf 41
Prime chain 20
Principal complex curvatures of a complex submanifold 253
Projective completion of an affine variety 2
Projective variety 2 8
Rational function 163
Rational normal curve 120
Rational surface 165
Resultant of two polynomials 97
Riemann conditions 127
Riemann — Hurwitz formula 110
Riemann — Roch theorem 117 158 144
Ringed spaces 214
Schubert cycles 221 223
Section 43
Section, holomorphic 58 63 67
Segre embedding 170
Sheaf 42 51
Sheaf, direct image 214
Sheaf, fine 47
Sheaf, germs of holomorphic sections 157
Siegel half space 128
Simple cusp 105
Simplical complex 26
Smooth point (nonsingular point) 18
Spectrum (prime ideals) 214
Steifel manifold 226
Stein factorization theorem 197
Stokes theorem 33
Surface, elliptic 198
Surface, Enriques 197 210
Surface, Hirzebruch 183
Surface, hyperelliptic 190
Surface, K-3 (exceptional) 193 199
Surface, Kummer 208
Surface, minimal 169 192
Surface, rational 183
Surface, ruled (geometrically) 169 176
Tangent number 104
Topologically singular point 93
Torelli theorem for curves 128
Torelli theorem for K-3 surfaces 202 206
Torus 126
Totally complex umbilic submanifold 256
Transcendence degree 20
Triangulation 27
Unirational projective varity 185
Universal coefficient theorem 30
Variety, abstract 14 15
Variety, affine algebraic 1
Variety, Albanese 186
Variety, analytic 15 48
Variety, projective algebraic 2 8
Vector bundle 51
Vector bundle, holomorphic 58
Veronese embedding 86 95 248
Veronese surface 26 262
Weak solution 36
Weierstrass point on a Riemann surface 134
Weierstrass polynomial 16
Weierstrass preparation theorem 16
Weyl formulae (generalized) 245
Whitney product formula for Chern classes 62
Wirtinger's theorem and the degree 79 162
Zariski topology 4
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