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| Newstead P.E. — Introduction to modulu problems and orbit spaces |
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| Предметный указатель |
1-parameter subgroup 103
Action of an algebraic group 43
Action, closed 43
Action, L-linear 82
Action, linear 44 73
Action, rational 47
Affine morphism 6
Affine open subset 3
Affine quotients 61—69
Affine variety 3
Algebraic group 42
Algebraic group, linear 44
Ample line bundle 33
Binary cubics 95 96
Binary forms 94—100 110 111
Binary quartios 96—100
Cate crical quotient 39
Closed action 43
Coarse moduli space 23 24
Cocycle condition 3 12
Cohomology of coherent sheaves over a curve 129—133
Compact variety 5
Compactification of a variety 6
Cubic curves 112—115
Cubic surfaces 115
Cubics, binary 95 96
Cyclic endomorphism of a vector space 36
Cyclic section 36
Cyclic vector 36
Degree of a coherent sheaf over a curve 130
Degree of a vector bundle over a curve 125 130
Determinant of a vector bundle 13
Direct sum of vector bundles 13
Discriminant 95 100
Dual of a vector bundle 13
Duality theorem 131
Embedding 3
Embedding, Segre 109
Endomorphism of a vector bundle 11
Endomorphism of a vector space, cyclic 36
Endomorphism of a vector space, semi-simple 31
Endomorphisms of vector spaces 28—41
Equivalence of families 19 20
Equivalence of families of vector bundles 146
Extension of vector bundles 126
Families 16—20
Family of endomorphisms of a vector space 23
Family of endomorphisms of complete varieties 18
Family of endomorphisms of hypersurfaces 17
Family of endomorphisms of torsion-free sheaves 167
Family of endomorphisms of vector bundles 19 125
Family, induced 20
Family, universal 23
Fibre of a torsion-free sheaf 164 165
Fine moduli space 22
Finite morphism 6
Flat morphias 9
Flat sheaf 9
Generic isomorphism of vector bundles over a curve 131
Generically surjeotive homomorphism of vector bundles over a curve 131
Geometric quotient 70
Geometrically reductive group 48
Good quotient 70
Grassmannian 119
G—invariant morphism 44
G—morphism 43 44
Hilbert polynomial of a coherent sheaf 130
Hilbert'e fourteenth problem 47 91
Homomorphism of algebraic groups 42
Homomorphism of vector bundles 11
Hyperplane bundle 13
Hypersurface in  8
Hypersurface, non-singular 8
Hypersurfaces 100
Hypersurfaces, quadric 93 94
Indecomposable vector bundle 126
Induced vector bundle 11 12
Induoed family 20
Invariant morphism 44
Invariant point 43
Invariant polynomial 48
Invariant subset 43
Isomorphism of families of vector bundles 125
Isomorphism of vector bundles 11
Jump phenomenon 26
L-linear action 82
Line bundle 10
Line bundle, ample 63
Linear action 44 73
Linear algebraic group 44
Linearisation of an action 7
Linearisation of an action of PGL(m) 87
| Linearisation of an action with respect to L 81
Linearly reductive group 48
Local universal property 37 38
Locally trivial morphism 10
Moduli problem 19
Moduli space, coarse 23 24
Moduli space, fine 22
Morphism, affine 6
Morphism, finite 6
Morphism, flat 9
Morphism, G- 43 44
Morphism, G-invariant 44
Morphism, locally trivial 10
Morphism, proper 6
Mumford's Conjecture 50 92
Nagata's theorem 49 52—61
Non-singular hypersurface 8
Orbit 43
Orbit space 39
Ordered seta of points of P 115—119
Plane cubic curves 112—115
Prevariety 3
Prevariety, separated 3
Projective quotients 70—81
Projeotive variety 3
Proper morphism 6
Quadrio hypersurfaces 93 94
Quasl-projective variety 3
Quotient, categorical 39
Quotient, geometric 70
Quotient, good 70
Quotients, affine 61—69
Quotients, projective 70—81
Rank of a coherent sheaf 129
Rank of a vector bundle 10
Rational action 47
Rational representation 44
Reductive group 48 50
Regular function 4
Regular point 66
Riamann — Hoch formula 130
Section of a vector bundle 11
Segre enbedding 109
Semi-aiaple endomorphism of a vector space 31
Semi-reductive group 48
Semi-stable point 73 82
Semi-stable torsion-free sheaf over a curve 165
Send-stable vector bundle over a curve 133
Separated prevariety 3
Sequences of linear subspaces 119—123
Simple vaotor bundle 127
Singular point of a hyper-surface 3
Stabiliser 43
Stability of binary cubics 95 96
Stability of binary forms 110 111
Stability of binary quartics 96—100
Stability of hypersurfaces 100
Stability of ordered sets of P 115—119
Stability of plane cubic curves 112—115
Stability of quadric hypersurfaces 93 94
Stability of sequences of linear subspaces 119—123
Stability of torsion-fres sheaves over a curve 164—170
Stability of vector bundles over a curve 124—170
Stable point 74 82
Stable torsion-free sheaf over a curve 165
Stable vector bundle over a curve 133
Subbundle generically generated by a subsheaf 132
Subbundle generically generated by a subspace of  133
Subbundle of a torsion-free sheaf 164
Tensor produot of vector bundles 13
Torsion-free sheaf over a curve, semi-stable 165
Torsion-free sheaf over a curve, stable 165
Torsion-free sheaves over a curve 164—170
Trivial bundle 11
Trivialiaatlon 10
Universal fandly 23
Valuative oritarion for props mass 7 3
Variety 2
Variety, affine 3
Variety, complete 5
Variety, projetive 3
Variety, quasi-projective 3
Vector bundle 10
Vector bundle over a curve generated by its sections 132
Vector bundle over a curve generically generated by its sections 132
Vector bundle over a curve, indecomposable 126
Vector bundle over a curve, semi-stable 133
Vector bundle over a curve, simple 127
Vector bundle over a curve, stable 133
Vector bundle, induced 11 12
Vector bundle, trivial 11
Vector bundles over a curve 124—170
Zariski topology 3
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