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

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Год издания: 1982

Количество страниц: 347

Добавлена в каталог: 18.11.2009

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Предметный указатель

$Aff_{n}(k)$       65 289
$J_{2}(k)$       66 289
$T_{0}$ -space      13 15 25 241
$\kappa$ -calculus      307
$\kappa(D, S)$       269
$\kappa(D, V)$       298
$\kappa(S)$       271
$\kappa(V)$       309
$\mathbb{Q}$ -topology      16
$\mathcal{O}$ -homomorphism      29
$\mathcal{O}$ -ideals      59
$\mathcal{O}$ -module      28—29
$\mathcal{O}$ -module, coherent      47—48 181 230
$\mathcal{O}$ -module, finite type      46
$\mathcal{O}$ -module, free      44
$\mathcal{O}$ -module, quasi-coherent      45
$\overline{A}$ -homomorphism      42
$\overline{A}$ -modules associated with M      42
Abelian variety      308 312
Adjunction formula      201
Adjunction formula, generalized      204—205
Affine algebraic curve      51
Affine algebraic group      340
Affine algebraic variety      51 100
Affine morphism      88—89 94
Affine n-space      42 100
Affine Noetherian scheme      50
Affine open cover      55
Affine open subset      54
Affine scheme      4 41 179
Affine scheme, algebraic      51
Affine scheme, integral      51
Affine scheme, morphism of      53
Affine scheme, reduced      50—51
algebraic      19 87
Algebraic affine scheme      51
Algebraic boundary      99
Algebraic over R      87
Algebraic torus      326
Algebraic variety      95
ample      156 235
Ample divisor      156
Ample divisor, very      156 216—217
Ample, f-      239
Ample, R-      236
Arithmetic Euler — Poincare characteristic      182
Arithmetic genus      182
Artinian local ring      26
Artinian ring      26
Auslander Buchsbaum      120
Automorphism group      65
Base extension      71 75 77 86 89 91 93
Base extension of L      151
Base extension, locus      128
Base extension, number      266
Base extension, point      128
Base extension, scheme      65
Bertini      250
Bigenus      199
Birational automorphism group      96
Birational map      96
Birationally equivalent      96
Birationally equivalent, proper      137
Canonical derivation      188—189
Canonical divisor      199 208
Canonical fibered variety      311
Canonical homomorphism      10 34 145
Canonical involution      224
Canonical projection      64
Canonical rational map      200
Cartier sheaf      153
Castelnuovo      265 297
Category of S-schemes      65
Characteristic pair, first      285
Characteristic pairs of a cusp      285
Characteristic polynomials      113
Chinese remainder theorem      26 143
Chow's Lemma      137 170
Class of a curve      294
Clebsch      280
Clifford      213
Closed image      83
Closed immersion      61 71—72 76 86 89—93 241
Closed morphism      90
Closed morphism, universally      90
Closed point      15 20 84
Closed subscheme      60
Closure      14 15
Closure, scheme      92
Codimension      22
Cohen      23
Coherence, local property of      49
Coherent      47—48 181 230
Cohomology      176 226 230
Cokernel      36
complete      92 94—95 100
Complete linear system      127
Complete local ring      113
Completion      99 113 258
Composition of morphisms      52
Composition of rational maps      82
Conductor      204-205
Connectedness theorem of Zariski      138
Constant sheaf      28 152
Coordinate cover      196
Coordinate neighborhood      195
Coordinate system, local      195
Covering theorem      304 311 341
Covering, double      216—218
Covering, r-sheeted      216
Curve      100 208
Curve, affine algebraic      51
Curve, hyperelliptic      217
Cusp      281
Cusp, simple      281
D-canonical fibered variety      303
D-dimension      298
D-index      220
de Jonquierre transformation      289
Degenerary principle of Enriques      138
Degree of a curve      213
Degree of a polynomial      2
Degree of a rational map      143
Degree of an invertible sheaf      185
Degree of V      274
Derivation      189
Derivation, rule      189
Derived functions      221
Diagonal morphism      72 194
Difference kernel      74
Differential      189
Differential form      189 196
Differential form, rational      196
Differential form, regular      196
DIMENSION      22
Dimension of ringed space      42
Direct image sheaf      52 88
Direct sum      44 172
Discrete valuation      122
Discrete valuation ring      122
Divisor      125
Divisor defined by $\varphi$       125
Divisor defined by a section      154
Divisor group      125
Divisor, ample      156
Divisor, canonical      199
Divisor, effective      125
Divisor, exceptional      158
Divisor, horizontal      300
Divisor, locally principal      155

Divisor, negative part of      125
Divisor, positive part of      125
Divisor, prime      124
Divisor, principal      125
Divisor, pull back of      130 132
Divisor, ramification      202
Divisor, reduced      257
Divisor, vertical      300
Divisor, very ample      156
Divisor, very ample, with simple normal crossings      257
Domain of rational function      79
Dominating      9 83
Dominating morphism      71
Dominating rational map      96
Dual curve      291
Dual homogeneous polynomial      291
Dynkin diagram      307
Dynkin type, reduced curve of      307 333
Easy addition theorem      303 310
Elliptic type      311
Embedded prime ideal      109
Enriques      138
Etale covering      248 338
Etale covering, endomorphism      336
Etale covering, map      30
Etale covering, morphism      248
Etale covering, space      30
Euclidean algorithm      5 286 288
Euler — Poincare characteristic      182
Exact presheaf      35
Exact sheaf      35
Exceptional divisor with respect to f      158
Extending base scheme      71
Extension theorem      124
Exterior power      194
f.g. type      84
Factorial ring      106
Fiber      73
Fiber type      312
Fiber, general      250
Fiber, generic      74
Fiber, product      70
Fibered variety      299 338
Fibered variety, canonical      311
Fibered variety, D-canonical      303
Fibered variety, proper      299
Fibered variety, proper smooth      299
Fibering theorem      302 310
Field of fractions      10
Field, residue class      12
Finite homomorphism      93
Finite morphism      92—93
Finite presentation      227
Finite type at a point      46—47
Finite type, of      85—86
Finitely generated graded algebra      162
Finitely generated graded ring      162
Finitely generated over R      162
Finiteness theorem      239 243
Fixed component      130
Fixed point      130
Flabby      177
Flex      244
Form, logarithmic      320
Form, rational      188
Form, regular      188 194
Fractions, module of      10
Free $\mathcal{O}$ -module      44
Free A-module, graded      227
Fujita      211 318
Function field      95
Function field, rational      79
Fundamental sheaf      166
Gap sequence      219
General fiber      250
General member      250
General point      250
General type, of      311
Generator      46
Generic fiber      74
Generic point      15 34 74 83 291
Genus      208
Genus, arithmetic      182
Genus, formula of Clebsch      280
Genus, formula of Riemann      217
Genus, geometric      199
Genus, m      199
Genus, virtual      265
Geometric model      96
Germ      28
Glueing lemma      62
Glueing of morphisms      57
Graded A-module      160
Graded algebra, finitely generated      162
Graded free A-module      227
Graded R-algebra      160
Graded ring      160
Graph      72—73 76 133
Graph of rational map      133
Grothendieck      134 138 179 181 243
Group of numerical classes of divisors      266
Gutwirth      287
Hartogs      124
Height      23 107
hilbert      19 21 49 112 227 245
Hilbert nullstellensatz      19—20
Hironaka      255
Hirzebrush      182
Hodge's index theorem      267
Homogeneous coordinate system      63—64
Homogeneous element      160
Homogeneous ideal      160
Homogeneous spectrum      161
Homomorphism of presheaves      29
Homomorphism of sheaves      29
Homomorphism, $\alpha$       226—227
Homomorphism, $\beta$       228—229
Homomorphism, canonical      10 34
Homomorphism, finite      93
Homomorphism, identity      29
Homomorphism, local      30 52
Hopf      295
Horizontal divisor      300
Hurwitz      216 224—225
Hyperbolic type, of      311
Hyperelliptic curve      217
Hyperplane section      150 214—215
Hypersurface      156
i      266
Ideals, sheaf of      59
Identity      29 52
Image, closed      83
Image, presheaf      33
Image, sheaf      33
Image, sheaf, direct      52 88
Immersion      61 71 77 93
Immersion, closed      61 71 76 86 89—91 93
Immersion, open      61 71 99
Index (D-)      220
Index of I      266
Index of speciality      212
Infinitely near points      278
Infinitely near singular point      279—280
Inflexion, point of      294
Initial form      118
Injective $\mathcal{O}_{x}$ -module      174
Injective limit      28
Injective resolution      175
Injective sheaf      174
Injective theorem      175

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