Kempf G.R. — Algebraic Varieties :: Электронная библиотека попечительского совета мехмата МГУ

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Kempf G.R. — Algebraic Varieties

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Название: Algebraic Varieties

Автор: Kempf G.R.

Аннотация:

In this book Professor Kempf gives an introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint. By taking this view he is able to give a clean and lucid account of the subject which will be easily accessible to all newcomers to algebraic varieties, graduate students or experts from other fields alike. Anyone who goes on to study schemes will find that this book is an ideal preparatory text.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1993

Количество страниц: 173

Добавлена в каталог: 20.05.2008

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Предметный указатель

$Cot_x(X) \equiv m_x/m_x^2$ , the Zariski cotangent space of X at x      70
$talk exactness      47
\theta_x$      43
$\mathbb{G}_m$ -invariant      31
(f, f*)-homomorphism      66
A-invariant subspace      142
Abelian sheaf      46
Abelian variety      35
Additive functor      98
Adjoint      66 134
Adjunction formula      79
Affine line      3
Affine morphism      18
Affine nullstellensatz      5
Affine smooth curve      86
Affine u-space      10
Affine variety      3
Algebraic group      30
Ample invertible sheaves      68
Arithmetic genus of C      127
Ascending chain condition      62
Associated sheaf       44
Associated sheaf $M\otimes_{\mathcal{A}(x)}\mathcal{A}$       55
Associated sheaf $Sym^n \mathcal{M}$       55
Basis for a topology      5 7 32
Bertini’s theorem      83
Bezout’s Theorem      126
Biadditive      135
Birational morphism      34
Blown up affine space      36
C(X) cone over a closed set X      31
Canonical quotient short exact sequences of flabby sheaves      47
Categorical product      25
Cauchy residue      110
Cech cohomology      115
Chain condition      15
Characteristic of k is prime      94
Chow covering      89 130
Chow’s Lemma      34
Closed mapping      132
Coherent $\mathcal{O}_Y$ -module $\mathcal{I}_{X|\Delta}\equiv\mathcal{I}_X\mathcal{I}^2_X$ annihilated by $\mathcal{I}_X$       59
Coherent module      58
Cohomology class      100
Cohomology group $H^1(C,\mathcal{F})$       97
Cohomology group $H^i(X,\mathcal{F})$       98
Complete variety      33
Complex $D*(\mathcal{F})$       98
Complex $\Gamma(X, D*\mathcal{F})$       98
Component of a topological space      17
Cone      31
Connected topological space      16
Constant sheaf $Rat(\mathcal{F})$ for a coherent $\mathcal{F}$       90
Coordinate filtration      126
Correspondence      132
Cousin problem      96
Cramer’s Rule      6
Curve $\equiv$ irreductible separated one-dimensional variety      85
Cusp      75
Decent presheaf      41
Degree of a divisor      90
Degree of an invertible sheaf on a singular curve      93
Degree of an invertible sheaf on a smooth curve      93
Dense      18
Descending chain condition      16
Determinantal varieties      11
Determinants of all $(r + 1) \times (r + 1)$ submatrices of $\alpha$       12
Diagonal embedding      59
Differential form      72
Differential,       70
Differentials      49
Dimension of a topological space      20
Direct limit      50
Direct limit of sheaves      50
Direct sum      54
Direct system      141
Direct system of sheaves      50
Discontinuous sections      40
Discrete valuatipn ring (DVR)      85
divisors      63
Effective divisor      63
Eigenvalues      142
Eigenvectors      142
Elliptic curve      35 128
Euler characteristic $\chi(\mathcal{F})$ of $\mathcal{F}$       117
Euler exact sequence      48
Evaluation of a function at a point      8
Exact sequence of abelian sheaves      47
Exceptional divisor $E = \pi^{-1}_{\mathbb{A}^n}({0})$ at the origin      37
Exterior power $\Lambda^n \mathcal{M}$       55
f-homomorphism      66
Field k(X) of rational functions on irreductible X      62
Filtration by coherent sheaves      91
Finite morphism      18
Finite surjective morphism      20
Finitely generated torsional $\mathcal{O}_{C,c_i}$ -modules      91
First order variation of a function at x      70
Flabby resolution      102
Flabby sheaves      46
Flat module      118
Flat sheaf over Y      118
Fractional ideals      63
Free $\mathcal{A}$ -modules      55
Free Abelian group      63
Function field of dimension one      88
Genus of a curve      104
Global invariant $Cok(\alpha)$ of the sheaf $\mathcal{F}$       97
Global section $\Gamma$       94
Global statements      93
Godement’s canonical flabby resolutions      46
Graded module      61
Graded ring      61
Graph(f)      88
Grauert      121
Grothendieck      118
Higher direct image $R^if_*\mathcal{F}$       102
Hilbert’s basis theorem      15
Hilbert’s Nullstellensatz      5
Hirzebruch      117
Hirzebruch — Riemann — Roch theorem      117
Homogeneous      11
Homogeneous coordinate      28
Homogeneous equation      126
Homomorphism of abelian (pre-)sheaves      46
Homotopically trivial      115
Hyperelliptic curves      109
Hyperplane      83
Hypersurface      21
i-th cohomology group $H^i(X, \mathcal{F})$       98
Ideal sheaf      59
Implicit differentiation      76
Increasing sequence of ideals in the noetherian ring      86
Induced structure of a space with functions      9
Integral closure in quotient field      89
Integral closure, commutes with localization      83
Integral domain      16
Intersection multiplicity I(C, D: p) of C and D at p      127
Intersection number      127
Invertible $\mathcal{A}$ -module      55
Invertible fractional ideals IFI(X) of       63
Invertible ideals of $\mathcal{O}_X$       64
Invertible sheaves      62
Irreducible divisors      63
Irreducible topological space      16
Isolated point = a component      20
Isomorphism of spaces with functions      2
Kunneth formula      114
Lagrange identity      111
Left exact      67
Leray      38

Leray spectral sequence      134
Limiting secant      73
Linear change of variables      13
Local coordinates      28
localization      6
Locally closed      29
Locally factorial      64
Locally free $\mathcal{A}$ -module      55
Locally free $\mathcal{O}_D$ -module of rank degf      92
Locally free coherent sheaf on a smooth curve      92
Locally regular      1
Locally trivial bundle of lines      37
Locally vanishing principle      100
Locus      32
Long division      14
Long exact sequence of homology groups      99
Lower-semicontinuous      12
Luroth      110
Mapping cone      119
Matrix $(F*\psi_{ij})$       67
Matrix of sections      55
Minimal prime ideal      17
Morphism of presheaves      38
Morphism of spaces with functions      2
Morphism of varieties      3
Multiplicative subset      7
Mumford’s rigidity      132
Nakayama’s Lemma      6
Nilpotent      4
Node      75
Noether      5
Noetherian Induction      52
Noetherian local ring      74
Noetherian topological space      15
Noether’s Normalization Lemma      83
Non-degenerate symmetric k(D)-bilinear form on k(C)      94
Normal variety      82
Normalization of a variety X in k(X)      82
Nullstellensatz      5
Obstruction to solving the Cousin problem      104
Open affine subvarieties      11
Open subspace of a space with functions      2
Ordinary sheaf      97
parabola      75
Partially ordered set      39
Patching condition      41
Picard group of X, Pic(X)      62
Plane curves      127
Preparation lemma      13
Presentation of $\mathcal{M}$       58
Presheaf      38
Principal fractional ideals P(X) of       63
Principal ideal theorem      22
Principal part of $\omega$ at c      110
Principal parts at c of rational sections of $\mathcal{F}$       96
Products      25
Projective embedding      125
Projective line $\mathbb{P}^1$       3
Projective n-space $\mathbb{P}^n$       11
Projective nullstellensatz      32
Projective space $\mathbb{P}^{n*}$       83
Projective subvariety      31
Proof of Lemma 1.4.1      14
Proof of Lemma 1.5.6      15
Punctured affine space $\mathbb{A}^n - {0}$       10
Pure dimension      79
Purely inseparable morphism      94
Quadratic function on the group of correspondence      135
Quasi-affine variety      10
Quasi-coherent      55
Quasi-compact      7
Quasi-projective variety      11
Quotient space with functions      10
Radical Rad(A) of A      5
Radical vector field      79
Ramification index      94
Ramified at c      94
Ramified morphism      94
Rank      55
Rank, finite      55
Rational differential      110
Rational mapping      89
Reduction to the diagonal      33
Regular function      1
Regular rational mapping      130
Residue $Res_c(\omega)$ of a rational differential $\omega$ at c      110
Restriction $\mathcal{A}|_U$ of $\mathcal{A}$ to U      55
Restriction $\mathcal{M}|_U$ of $\mathcal{A}$ -module $\mathcal{M}$ to U      55
Riemann — Hurwitz Theorem      109
Riemann — Roch theorem      98
Right exact      67
Secant       73
Section      39
Segre embedding theorem      27
Semi-positive quadratic forms      137
Separable morphism      94
Separated varieties      29
Serre      101
Serre duality      107
Serre vanishing theorem      125
Sheaf      41
Sheaf $Prin(\mathcal{F})$ of principal parts      96
Sheaf $\mathcal{O}_X$ of regular functions on X      54
Sheaf A of rings      54
Sheaf of $C^{\infty}$ functions      49
Sheaf of $\mathcal{A}$ -modules      54
Sheaf of differentials      60
Sheaf of fractional ideals J of Ratjv      63
Sheafification      44
Short exact sequence of abelian sheaves      47
Singular curve      127
Singular point      84
Skyscraper sheaf $R^if_*(\mathcal{F}_y)$       120
Smooth at a point      79
Smooth complete curve      92
Smooth completion of G      131
Smooth curve      86
Smooth divisor      79
Smooth projective curve      88
Smooth variety      71
Snake homomorphism      120
Space with functions      1
Stalk       39
Sub-(pre-)sheaf      42
Subvariety      9
Support of $\mathcal{F}$       53
Syzygies      65
Tame ramification point of f      95
Tangent cone, $(TC_xX)_{red}$       73
Tangent space      71
Tangent vector      131
Torsion-free sheaf      91
Torsional coherent sheaf      91
Torsional element      91
Torsional sheaf      91
Translation by g      69
Twisted sheaf $\mathcal{F}(m)$       60
Unique factorization domain (UFD)      21
Unramified morphism      94
Upper-semicontinuous      61
Variational cohomology of a constant family of sheaves      103
Variety (algebraic)      3
Vector field      79
Vector space $\mathcal{F}|_x$ at a point x      60
Very ample invertible sheaves      68
Weil divisors      63
Weil — Riemann — Roch theorem      108
Weil’s Riemann hypothesis      137
Zariski cotangent space      70
Zero divisor of $\psi$       134

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