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Sertoz S. — Algebraic Geometry
Sertoz S. — Algebraic Geometry

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Название: Algebraic Geometry

Автор: Sertoz S.

Аннотация:

This timely resource — based on the Summer School on Algebraic Geometry held recently at Bilkent University, Ankara, Turkey — surveys and applies fundamental ideas and techniques in the theory of curves, surfaces, and threefolds to a wide variety of subjects. Written by leading authorities representing distinguished institutions, Algebraic Geometry furnishes all the basic definitions necessary for understanding, provides interrelated articles that support and refer to one another, and covers weighted projective spaces...toric varieties...the Riemann-Kempf singularity theorem...McPherson's graph construction...Grobner techniques...complex multiplication...coding theory...and more. With over 1250 bibliographic citations, equations, and drawings, as well as an extensive index, Algebraic Geometry is an invaluable resource for algebraic geometers, algebraists, geometers, number theorists, topologists, theoretical physicists, and upper-level undergraduate and graduate students in these disciplines.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 382

Добавлена в каталог: 17.01.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$Specm(R_\sigma)$      60
$Z_\infty$      136
$\bar{\mathbb{P}}(E)$      see “Weighted projective bundle”
$\bar{\mathbb{P}}^n$      see “Weighted projective space”
$\mathbb{P}_\mathbb{C}(q_0,...,q_n)$      see “Weighted projective space”
$\mathbb{Q}$-factorial      304
1-form      96
1-form holomorphic      98
Abel      266 268
Abel's theorem      117 118 120 126
Abelian differential      112
Abelian map      120
Abelian surfaces      188
Affine algebraic set      59
Affine toric varieties      60
Algebraic canonical class of surface      166
Algebraic curve      160
Algebraic divisors on surface      164
Algebraic function      109
Algebraic numerical invariants of surface      168
Algebraic Picard group of surface      165
Algebraic plurigenera surface      166
Algebraic set      220
Algebraic surface      161
Amrani, A.      1
Analytically equivalent      222
Anecdote      ii
Anti-graded lex order      247
Artinian sheaf      355
Bernoulli Brothers      259
Bernoulli numbers      283
Betti numbers      168
Bielliptic surfaces      194
Big divisor      303
Blowup      174
Bogomolov — Miyaoka — Yau inequality      206
Bogomolov — Miyaoka — Yau line (BMY)      211
Branch point      104
Brasselet, J.-P.      53
Canonical curve      127
Canonical models      213
Canonical singularities      302
Cartier divisor      79 298
Castelnuovo      176
Cauchy's integral formula      99
Cauchy's lemma      98
Character incomplete sum      315
Character sum      314
Clebsch curve      352
Complete intersections      207
Complex multiplication      269
Concert      ii
Cone      54 223
Cone dual      55
Cone of curves      300
Cone theorem      308
Cone, edge of      56
Cone, exceptional      229
Cone, face of      56
Cone, regular      73
Cone, simplex      73
Cone, strongly convex      55
Coordinate ring      59
Cubic surface      186
Darboux curve      352
Degree      173
Degree-anticompatible ordering      246
Del Pezzo surface      187
Differential $d\omega$      97
Difficulty      306
Disquisitiones Arithmeticae      266 267 224 277
Donaldson numbers      373
Double cover of the plane      208
Du Val singularities      213
Dynkin diagrams      199 214
Eagon — Northcott resolution      360
Ecart      252
Eisenstein series      269
Eisenstein's criterion      275
Eisenstein's theorem      2 76
Elementary transformation      182
Elliptic function      230
Elliptic integral      265
Elliptic surfaces      196
Enriques surfaces      192
Euler      108 261
Euler number      168
Euler-Poincare characteristic      170
Extremal ray      300
Fagnano      261
Fan      56
Fan, complete      74
Fan, polytopal      74
Fan, regular      74
Fermat      273
Fields medal      291
Fitting ideals      138
Flip      305
FLOP      307
Frobenius automorphism      277
Fun, simplicial      73
Fundamental group      102
Galois      266
Gauss      266
Genus formula      173
Geometrically ruled      182
Gilbert-Varshamov bound      318
Godeaux surfaces      212
Gomez-Mont, X.      89
Goppa code      317
Gordon's lemma      57
Graph construction      135—136
Graph construction for a sheaf      146
Graph construction, analyticity      141—142
Groebner basis      235 249
Hecke L-series      283
Hilbert scheme      367
Hironaka      291
Hirzebruch surface      72 183
Hodge index theorem      173
Homotopic      98
Horikawa surface      210
Horikawa's analysis      209
Hurwitz      282
Hyperelliptic      124
Hyperelliptic surfaces      194
Hypersurface      222
Ideal membership problem      231
Index theorem      172
Intersection theory      172
Irregularity      168
J-function      200
jacobi      264
Jacobian      115
Jacobian surfaces      197
Jacobian variety      90
Jumping line      365
K-theory classes      151
K3 surfaces      189
K3 surfaces in projective space      191
K3 surfaces, curves on      192
K3 surfaces, moduli      191
Kawamata      304
Kodaira dimension      167
Kodaira's classification      198
Kummer surfaces      190
Kwieciniski, M.      135
Lattice cone      54
Leading term      233
Lefschetz (1, 1)-theorem      170
legendre      261
Lemniscate      259
Lemniscate, arc length of      261
Lexicographic ordering      232
Link of a singularity      223
Local ordering      247
Lueroth quartics      353
Mather class      149—150 151
Maximum Modulus Principle      99
Mean value property      99
Milnor fibre      241
Milnor number      240
Minimal Model Program      307
Minimal surface      176
Miranda, R.      157
MMP      see “Minimal Model Program”
Modified fibre product      143
Monoid      56
Monoid, finitely generated      57
Mori      177 291 301 305
Multiplicative ordering      232
Nash transform      144
Nef      300
Neron — Severi group      170
Noether's formula      173
Noether's inequality      206
Noncommutative plane      363
Nullstellensatz      59
Numerical equivalence      299
O'Shea, D.      219
Period      102 115
Persson      207
Picard group      298
Picard number      299
Poincare morphism      83
Polyhedral cone      54
Primitive vector in $\mathbb{Z}^n$      73
Proclus      258
Projective plane      178
Pseudovariety      83
Quadric surfaces      179
Quintic surfaces      212
Ramification index      104
Rational double points      213
Rational normal curve      184
Rational normal scroll      185
Reciprocity law      278
Reflexive sheaf      355
Regular pair      358
Regular polygon      358
Reid      292 303
Residue      100 103
Riemann hypothesis      315
Riemann sphere      105
Riemann surface      106 160
Riemann — Hurwitz formula      108
Riemann — Kempf singularity theorem      131
Riemann — Roch theorem      128 172 173
Ruled surfaces      181
Schappacher, N.      257
Scheme at infinity      147
Schwartz — MacPherson class      86
SCROLL      185
Separating points      160
Separating tangents      160
Sertoez, S.      291
Shokurov      306
Siegel      262
Signature theorem      172
Singularity      100
Stepanov, S.      313
Stokes' theorem      97
Tangent cone      226
Tangent space      225
Terminal singularities      303
Thom-Hirzebruch index theorem      172
Tjurina number      241
Topologically equivalent      222
Toric variety      65 69
Torsion free sheaf      355
Torsion sheaf      355
TUBITAK      ii
Twisted projective space      see “weighted projective space”
Tyurin moral      377
Tyurin slogan      348
Tyurin, A.      347
Universal Abelian integral      90 111 115
Vanishing ideal of X      59
Variety      220
Weierstrass      269
Weierstrass $\wp$-function      270
Weierstrass equations      197
Weighted projective bundle      44
Weighted projective bundle, cohomology of      46
Weighted projective space      5 73
Weighted projective space as a scheme      32
Weighted projective space as geometric quotients      28
Weighted projective space, cellular decomposition of      8
Weighted projective space, cohomology of      16
Weighted projective space, etale cohomology of      42
Weil      314
Weil divisor      79 298
Whitney's theorem      2 2 1
Zariski conjecture      242
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