Yang K. — Complex Algebraic Geometry: An Introduction to Curves and Surfaces :: Электронная библиотека попечительского совета мехмата МГУ

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Yang K. — Complex Algebraic Geometry: An Introduction to Curves and Surfaces

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Название: Complex Algebraic Geometry: An Introduction to Curves and Surfaces

Автор: Yang K.

Аннотация:

A textbook for second-year graduate students who are familiar with algebraic topology, function theory, and elementary differential geometry. The collection of seminar notes constitutes an introduction to complex algebraic geometry, focusing on its transcendental aspect.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 301

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

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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