Ueno K. — An Introduction to Algebraic Geometry (Translations of Mathematical Monographs) :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Ueno K. — An Introduction to Algebraic Geometry (Translations of Mathematical Monographs)

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: An Introduction to Algebraic Geometry (Translations of Mathematical Monographs)

Автор: Ueno K.

Аннотация:

This introduction to algebraic geometry allows readers to grasp the fundamentals of the subject with only linear algebra and calculus as prerequisites. After a brief history of the subject, the book introduces projective spaces and projective varieties, and explains plane curves and resolution of their singularities. The volume further develops the geometry of algebraic curves and treats congruence zeta functions of algebraic curves over a finite field. It concludes with a complex analytical discussion of algebraic curves. The author emphasizes computation of concrete examples rather than proofs, and these examples are discussed from various viewpoints. This approach allows readers to develop a deeper understanding of the theorems.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 246

Добавлена в каталог: 17.06.2008

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

Предметный указатель

Abel's theorem      199
Abelian function theory      43
Affine plane      58 73
Affine plane curve      66
Affine plane, complex      58
Affine transformation      8
Affine transformation group      8
Algebraic curve      135
Algebraic geometry      64
Algebraic morphism      29 70 147
Algebraically closed field      228
Almost everywhere      72 103
Analytic set      180
Atiyah — Singer index theorem      185
Base point      36 177
Bezout's theorem      34
Birational equivalence      106
Birational geometry      44
Birational mapping      72
Birational transformation      64
Bitangent      43
Blow-up      115
Blowing-up      117 119 127
Branch, of a curve      81
Canonical curve      155
Canonical divisor      142 185
Canonical map      154
Characteristic      228
Chow's theorem      180
Class of a curve      38
Commutative field      213 219 220
Commutative ring      210 220
Complete linear system      177
Complex manifold      85 179
Complex projective space      91
Complex torus, one-dimensional      182 187
Complex torus, q-dimensional      197
Congruence modulo a number      207
Congruence transformation      6
Congruence zeta function      167
Coordinate neighborhood      180
Covering surface      44
Cremona transformation      71
Curve defined over a subfield      160
Cusp of type (2,3)      80
Cusp of type (2,5)      126
Cusp of type (p,q)      126
Defining equation      65 95
Degree of a differential form      142
Degree of a divisor      136 184
Degree of a plane curve      23 65
Degree of a regular mapping      149
Degree of a surface      93
Discriminant      158
Divisor      135 182
Divisor, canonical      142 184
Divisor, positive      141
Divisor, principal      137 183
Dual curve      38
Dual projective plane      38 61
Duality principle      43
Elliptic curve      140 160
Elliptic curve, defining equation of      160
Elliptic function      182
Elliptic function field      91
Euclidean transformation      6
Euler's identity      46
Exceptional curve      115
Exceptional surface      128
Fermat      48
Field      213
Field of definition      160
Field of quotients      234
Field, finite      229
Finite extension      105
Formal Laurent series      237
Formal power series      149 236
Formula of Hurwitz      149 151 177
Frey curve      48 178
Function field      56 64 88 104
Fundamental period      182
Fundamental theorem of algebra      228
GAGA of Serre      57 182
Generalized Hurwitz theorem      151
Generators of an ideal      98
Genus      145 151 154 155 159 182
Group structure      162
Hilbert's basis theorem      99
Hilbert's zero point theorem      88 99 228
Hironaka's theorem      127
Holomorphic differential form      181
Homogeneous component      98
Homogeneous coordinates      13 56 92
Homogeneous ideal      97
Homogeneous polynomial      18 56
Homology group      191
Homomorphism      223
Hurwitz theorem (formula)      see formula of Hurwitz
Hyperelliptic curve      140 154
Hyperelliptic function field      91
Hyperplane      92
Hyperplane at infinity      92
Hypersurface      93
Hypersurface of degree (d,e)      114
Hypersurface of degree d      93
Ideal      98 214 223
Ideal, generated by      223
Ideal, maximal      226
Ideal, prime      101 217 226
Identity element      220
Image      225
Imbedding      151
Inflection point      43 161
Inhomogeneous coordinates      13 92
Injection      69
Integral domain      226
Intersection multiplicity      34 85
Intersection number      190
Intersection theory      85
Inverse      212
Irreducible plane curve      23
Irreducible polynomial      23 213
Isolated singularity      129

Isomorphic curves      161
Isomorphism      160 224
J-invariant      158 160
Jacobian variety      198
K-rational point      166
Kernel      223
Legendre's canonical form      161
Line      60
Line at infinitiy      14 58
Linear equivalence      141 183
Linear frational transformation      9 53
Local intersection number      34 190
Local parameter      84 109
Local ring      233
Meromorphic differential form      181
Meromorphic differential form on a Riemann surface      181—182
Meromorphic function      57
Mordell-Weil theorem      57
Multiple point      see singular point
Multiple point of order n      32
Multiplicatively closed set      233
Multiplicity      31 78
n-fold point      33
Nonsingular plane curve      74
Nonsingular point      74
Nonsingular point of a plane curve      74
Nonsingular point of a variety      107
Normal rational curve      152
Normalized basis      196
Normalized period matrix      195
Ordinary cusp      33 79
Ordinary double point      33 79
Orthogonal group      5
Orthogonal matrix      5
Pencil      36
Period matrix      192 195
Plane curve      23 65
Plane curve of degree d      65
Plane curve, irreducible      23
Plane curve, reducible      23 65
Pliicker's formula      42
Point of indeterminancy      70
Polar curve      41
Pole      56 136
Pole of a differential form      142
Polynomial ring      98 222
Prime field      229
Prime ideal      101 217 226
Primitive element      232
Projection      10 102
Projective general linear group      55
Projective geometry      64
Projective line      25
Projective line, complex      27
Projective line, real      51
Projective plane      14 58
Projective plane, complex      22 58
Projective set      95
Projective set in $P |m \times P | n$       111 114
Projective set, irreducible      97
Projective set, reducible      97
Projective space      91
Projective submanifold      115
Projective transformation      15 24 54 62
Projective variety      97
Quadratic transformation      71
Quadric      67
Radical      99
Ramification index      148
Ramification point      148
Rank of an elliptic curve      165
Rational differential form      142
Rational function      57
Rational function in a projective variety      104
Rational function of n variables      104
Rational function on a plane curve      88
Rational function on P | 1 (C)      56
Rational function on P |2 (C)      64
Rational mapping      39 56 70 72
Reduced ideal      100
Regular differential form      142
Regular function      136
Regular mapping      70 147 see
Residue class      208 215 224
Residue ring      217 224
Resolution of singularities      116 120 127
Resolution of singularities for a plane curve      120 127
Resolution of singularities for a surface      127
Riemann      44 45
Riemann conjecture      168
Riemann constant      202
Riemann sphere      23 49
Riemann surface      44 85 180 181
Riemann — Roch theorem      145 185
Riemann's inequality      145
Riemann's relation      192
Riemann's singularity theorem      204
Scheme      48
Siegel's upper half-space      197
Singular point      32 74
Spec Z      48
Strict transform      122
Surjective injection      23
Symplectic basis      190
Symplectic group      196
Tangent cone      32 79
Tangent hyperplane      110
Tangent with multiplicity      31
Theta divisor      201
Theta function      200
Torsion subgroup      166
Total transform      122
Transcendental degree      105
Twisted cubic      96
Weierstrass canonical form      157
Weierstrass P-function      187
Weil's conjecture      168
Zariski topology      100
Zero divisor      212 217 226
Zero element      209 219
Zero of a differential form      142
Zero of a rational function      56 136
Zeta function      16

О проекте