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Miyanishi M. — Algebraic Geometry
Miyanishi M. — Algebraic Geometry



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Название: Algebraic Geometry

Автор: Miyanishi M.

Аннотация:

Students often find, in setting out to study algebraic geometry, that most of the serious textbooks on the subject require knowledge of ring theory, field theory, local rings and transcendental field extensions, and even sheaf theory. Often the expected background goes well beyond college mathematics. This book, aimed at senior undergraduates and graduate students, grew out of Miyanishi's attempt to lead students to an understanding of algebraic surfaces while presenting the necessary background along the way. Originally published in the Japanese in 1990, it presents a self-contained introduction to the fundamentals of algebraic geometry. This book begins with background on commutative algebras, sheaf theory, and related cohomology theory. The next part introduces schemes and algebraic varieties, the basic language of algebraic geometry. The last section brings readers to a point at which they can start to learn about the classification of algebraic surfaces


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 246

Добавлена в каталог: 01.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C_1$ -field      215
$P^1$-bundle      215
$P^1$-fibration      215
$P^1$-flber bundle      215
(-1) curve      199
Abelian presheaf      27
Abelian sheaf      29
Absolutely minimal model      208
Absolutely normal ring      184
Affine algebraic scheme      74
Affine algebraic set      73
Affine algebraic variety      74
Affine morphism      96
Affine open set      81
Affine scheme      61
Affine space      73
Algebraic curve      103
Algebraic scheme      89
Algebraic subvariety      89
Algebraic surface      152
Algebraic variety      89
Algebraically equivalent      187
Algebraically independent      3
Altitude theorem of Krull      24
ample      127
Arithmetic genus      160
Arithmetic genus formula      192
Ascending chain condition      9
Associated k-module      124
Base change      87
Base point      125
Birational invariant      197
Birational mapping      100
Blowing-up      169
Canonical divisor      151
Canonical sheaf      150 151
Cartier divisor      123
Cauchy sequence      133
Cech cochain      44
Cech cohomology      46
Cech n-coboundaries      45
Cech n-cocycles      45
Cech resolution      46
Closed embedding      81
Closed fiber      184
Closed immersion      81
Closed morphism      93
Closed subscheme      81
Codimension      64
Cofinal      133
Coherent      33
Cohomology      41
Cohomology functor      43
Cohomology theory      43
Cokernel      29
Compatible      26
Complete algebraic variety      92
Complete linear system      124
Completion      135
Composed of a pencil      180
Conormal sheaf      150
Contraction of the (-1) curve      201
Converge      134
Coordinate neighborhood      152
Coordinate ring      61 73
coordinates      73
Cross normally      168
Cross section      188 212
Cup product      154
Defining ideal      73
Degree      111 159
Degree n homomorphism      113
Del Pezzo surface      210
Derivation      143
Diagonal morphism      88
Differential module      144
Differential sheaf      150
DIMENSION      11
Dimension of linear system      124
Direct image      30 32 206
Direct sum      83
Discrete valuation      16
Discrete valuation ring      16
Divisor      121
Divisor class group      122
Domain of definition      99
Dominant      93
Dominant rational mapping      100
Double complex      50
Dual projective space      112
Dual sheaf      32
DVR      16
Effective divisor      121
Elementary transformation      219
Elliptic curve      163
Embedded prime divisor      14
Etale morphism      153
Euler — Poincare characteristic      159
Exact sequence of I-inductive systems      26
Exact sequence of presheaves      28
Exact sequence of sheaves      29
Exceptional curve      205
Exceptional curve of the first kind      169
Exceptional set      205
Extension      38
Factorization theorem of birational morphisms      204
Family of transition functions      120 121
Fiber      87
Fiber product      84
Fibration      184
Finite covering      96
Finite covering space      96
Finite morphism      96
Finitely generated      33
Finitely generated extension      3
Finitely generated morphism      89
Finitely generated Y-scheme      89
First theorem of Bertini      182
Fixed component      125
Fixed part      125
Flasque sheaf      47
Flat      71 88
Formula of Riemann — Hurwitz      162
Free basis      33
Function field      90
Generalization      81
Generic fiber      184 185
Generic point      63
Genus      160
Geometric genus      160
Geometric local ring      184
Going-up Theorem      12
Graded module      105
Graded ring      105
Graph      100
Ground field      159
Height      17
Higher direct image      42
Hirzebruch surface      218
Homogeneous      105
Homogeneous coordinates      110
Homogeneous ideal      105
Homogeneous part      106
Homogeneous spectrum      106
Homomorphism of degree 0      112
Homomorphism of presheaves      27
Homotopic      38
Hyperplane      111
Hypersurface      111
I-adic topology      136
Ideal quotient      14
Ideal sheaf      33
Idealization      79
Image      180
INDEX      122
Inductive limit      25
Inductive system      25
Infinitely near point      194
Infinitely near point of the first order      194
Injective module      37
Injective resolution      38
Injective system      37
integral      7
Integral closure      9
Integral extension      7
Integrally closed      9
Integrally closed integral domain      9
Intersection matrix      188
Intersection number      165
Invertible sheaf      115
Irrational pencil of curves      175
Irrational ruled surface      216
Irreducibility theorem      182
Irreducible      62
Irreducible component      63
Irreducible decomposition      64
Irreducible divisor      121
Irreducible ideal      13
Irreducible pencil      175
Irregularity      197
Irrelevant ideal      105
Jacobian criterion of nonsingularity      142
K-module      124
Kernel      29
Kodaira dimension      208
Krull dimension      11 62
Lemma of Artin — Rees      17
Length      4 62
Leray spectral sequences      54
Lifting      147
Lilnear subsystem      124
Linear pencil      182
Linear system      124
Linear topology      133
Llinearly equivalent      122
lnverse image      31 32
Local homomorphism      24
Local intersection multiplicity      167
Local ring      11
Local ringed space      31 32
Locally finitely generated morphism      89
Locally free      33
Locally free sheaf      120
Locally Noetherian scheme      97
Loop      215
Lueroth's theorem      20
Lying-over theorem      12
m-adic completion      137
Maximal condition      9
Maximal system of transcendental elements      4
Minimal algebraic surface      207
Minimal model      207
Minimal section      219
Module      32
Module of differential forms      144
Monoidal transformation      169
Morphism of affine algebraic sets      77
Morphism of affine schemes      62
Morphism of inductive systems      25
Morphism of local ringed space      32
Morphism of schemes      81
Morphism of sheaves      27
Multiple fiber      186
Multiplicative group      24
Multiplicity      169
N-genus      196
n-section      188
Nakai's criterion of ampleness      169
Nakayama's lemma      16
Neron — Severi group      197
Noether's normalization theorem      10
Noetherian domain, Noetherian      10
Noetherian space      62
Nonsingular      140
Nonsingular algebraic variety      141
Normal algebraic variety      97
Normal ring      15
Normal scheme      97
Normal sheaf      150
Normalization      9 98
Normalization morphism      98
Nullstellensatz of Hilbert      15
Numerically equivalent      197
Numerically equivalent to zero      197
Open immersion      81
Pencil      175
Pencil of curves      175
Picard group      120
Picard number      197
Polar divisor      122
Polar part      122
Presheaf      26
Presheaf (or a sheaf) of $\mathscr{A}$-modules      27
Primary ideal      13
Prime divisor      14
Prime divisor decomposition      14
Prime ideal sequence      11
Problem of Lueroth type      21
Problem of Zariski type      21
Projective algebraic variety      110
Projective bundle      211
Projective line      103
Projective module      37
Projective scheme      110
Projective space      110
Projective transformation      112
Projective transformation group      112
Proper      92
Proper morphism      93
Proper transform      101 170 171 205
Pull-back      127
Purely transcendental extension      3
Quasicoherent      33
Quasicompact      62
Quasicompact morphism      89
Ramification index      153
Rational algebraic surface      216
Rational curve      163
Rational function      74
Rational function field      3 74
Rational functions      3
Rational mapping      99
Rational mapping associated with linear system      125
Rational point      90
Rational surface      216
Reduced      74 82
Reduced divisor      121
Reduced form      82
Reducible      62
Reducible ideal      13
Reduction      87
refinement      45
Regular      74
Regular extension      6
Regular local ring      139
Regular system of parameters      139
Relatively minimal model      208
Restriction morphism      26
Riemann — Roch theorem      160
Ringed space      31
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