IItaka S. — Algebraic Geometry: An Introduction to Birational Geometry of Algebraic Varieties :: Электронная библиотека попечительского совета мехмата МГУ

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IItaka S. — Algebraic Geometry: An Introduction to Birational Geometry of Algebraic Varieties

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Название: Algebraic Geometry: An Introduction to Birational Geometry of Algebraic Varieties

Автор: IItaka S.

Аннотация:

The aim of this book is to introduce the reader to the geometric theory of algebraic varieties, in particular to the birational geometry of algebraic varieties.
This volume grew out of the author's book in Japanese published in 3 volumes by Iwanami, Tokyo, in 1977. While writing this English version, the author has tried to rearrange and rewrite the original material so that even beginners can read it easily without referring to other books, such as textbooks on commutative algebra. The reader is only expected to know the definition of Noetherin rings and the statement of the Hilbert basis theorem.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 347

Добавлена в каталог: 18.11.2009

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Предметный указатель

Separated scheme      78
Serre      48 120 179 206
Serre duality      206
Set of base points      128
Set of zeros of $\alpha$       152
Severi      182
Sheaf      27—28
Sheaf of Abelian groups      27
Sheaf of Abelian ideals      59
Sheaf of Abelian regular forms      194
Sheaf of Abelian sets      27
Sheaf of Abelian units      151
Sheaf of tensor product      37
Sheaf, ample invertible      235—236 239
Sheaf, associated with etale space      30
Sheaf, Cartier      153
Sheaf, coherent      47—48
Sheaf, constant      28
Sheaf, direct image      52 88
Sheaf, flabby      177
Sheaf, fundamental      166
Sheaf, homomorphism of      29
Sheaf, injective      174
Sheaf, inverse image      144
Sheaf, invertible      150
Sheaf, quasi-coherent      45
Sheaf, quotient      34
Sheaf, R-ample invertible      236
Sheaf, structure      41
Sheaf, tautological      166
Sheaf, very ample invertible      156
Sheafification      30—31 33—35
Signature of I      266
Simple cusp      281
Simple normal cross      257
Smooth at p      329
Smooth boundary      257 320
Smooth completion      258 320
Smooth morphism      249
Smooth part of f      300
Space, etale      30
Space, local ringed      41
Space, noetherian      14 241
Space, ringed      41
Space, Zariski tangent      117
Spec A      4
Special divisor      212
Speciality, index of      212
Spectral sequence      182—183
Spectrum      4
Spectrum, homogeneous      161
Stable under base extension      71 77 86 89—90 93
Stalk of etale space      30
Stalk of presheaf      28
Stein factorization theorem      141—142
Strict transform      256
Strictly birational automorphism group      325
Strictly integral      90
Strictly rational map      134—135 137 325

Structure morphism      65
Structure sheaf      41
Structure sheaf of projective scheme      165
Support of $\mathscr{F}$       47
Support of D      125
surface      100
Surface, affine algebraic      51
Tautological sheaf      166
Tensor product      11 37
Tensor product, presheaf      37
Tensor product, sheaf      37
Theorem A      236 239
Theorem B      236 238—239
Theorem, covering      304 310 341
Theorem, easy addition      303 310
Theorem, fibering      303 310
Theorem, finiteness      234 243 279
Theorem, Stein factorization      141—142
Theorem, uniqueness      311
Total deficiency      211 214
Total quotient ring      10
Transcendental degree      82 98 149
Tsunoda      149 299 318 344
Ueno      312 317 343
Unique factorization domain (UFD)      106—107
Uniqueness theorem      311
Units, sheaf of      151
Universal covering manifold      313
Universal mapping property of localization      8
Universal mapping property of tensor product      11
Universally closed morphism      90—91
Unscrewing lemma      241 243 271
Valuation, discrete      122 124
Variety      95
Variety of elliptic type      311
Variety of fiber type      312
Variety of general type      311
Variety of hyperbolic type      311
Variety of parabolic type      311
Variety, abelian      308
Variety, affine algebraic      51
Variety, algebraic      95
Variety, fibered      299
Variety, nonsingular      120
Variety, ruled      309
Vertical divisor      300
Very ample divisor      156
Very ample invertible sheaf      156
Virtual genus      265
Weber      224
Weierstrass divisor      222
Weierstrass form      222
Weierstrass point      219 220
Weierstrass preparation theorem      115
Weierstrass semigroup      219
Wronski form      221
Zariski      138 247 295
Zariski tangent space      117
Zeros of f      5 12 55 152
Zorn's lemma      6 14—15

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