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Dolgachev I. — Lectures on Invariant Theory
Dolgachev I. — Lectures on Invariant Theory

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Название: Lectures on Invariant Theory

Автор: Dolgachev I.

Аннотация:

This introduction to the main ideas of algebraic and geometric invariant theory assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, and the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples that originate in classical algebraic geometry. Written in an accessible style with many examples and exercises, the book offers a novel discussion of possible linearizations of actions and the variation of quotients under the change of linearization.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 220

Добавлена в каталог: 24.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$K$-point      36
$N$-fan      191
Absolute invariant      150 155 161
Action, faithful      89
Action, linearizable      124
Action, rational      37
Action, regular      37
Additive group      36 56 62 101
Adjugate matrix      18
Affine algebraic group      35
Affine cone      117 131
Algebra of covariants      70
Algebra of invariants      2
Algebraic group, diagonalizable      143
Algebraic group, exceptional type      42
Algebraic group, geometrically reductive      42
Algebraic group, linear      37
Algebraic group, linear reductive      42
Algebraic group, reductive      42
Algebraic group, semisimple      42
Algebraic group, simple      42
Algebraic torus      42
Algebraic variety, abstract      118
Algebraic variety, affine      35
Algebraic variety, complete      132
Algebraic variety, projective      40
Algebraic variety, proper      132
Algebraic variety, quasi-affine      50
Algebraic variety, quasi-projective      40
ample      103
Ample, very      103
Ampleness criterion      116
Apolar      15
Association isomorphism      181
Averaging operator      30 71
Base-point-free line bundle      103
Base-point-free linear system      111
Binary form      4
Bracket function      12 23
Capelli identity      28
Catalecticant      10 13 15 28 150
Catalecticant invariant      15
Catalecticant matrix      15
Cayley operator      17
Cayley-process      27
Cayley—Sylvester formula      82
Chamber      174
Chevalley’s criterion      100
Chow variety      100
Clebsch—Gordan decomposition      90
Closed embedding      40
Coaction homomorphism      37
Cocycle      104
Combinant      69 87
Complete reducibility      70
Concomitant      69
Contravariant      69
Convex polyhedral cone      188
Coordinate algebra      35
Covariant      66
Covariant of an action      69
Covariant, degree of      66
Covariant, order of      66
Cross-ratio      88 162 176
Diagonal action      65
Discriminant      9 14 15 26 28 68 146 147 149 150 152 154 161 163
Equivalence relation      91
Equivariant function      1
Exceptional curve      177
Fan      191
Fan, complete      193
Fan, simplicial      192
Flag complex      140
Flip      127 174
Fundamental Theorem, First      20 67
Fundamental Theorem, Second      24
G-variety      92
General points      61
Geometric grading      38
Gluing construction      117
Gluing data      117
Good Gm-action      38
Gordan—Hilbert Theorem      30
Group scheme      98
Haboush’s Theorem      42
Halphen pencil      59
Hankel determinant      10
Hermite Reciprocity      82
Hesse form      88
hessian      68 88
Highest weight      76
Highest weight module      76
Highest weight vector      76
Hilbert’s Problem      14 47
Hilbert—Mumford criterion      129
Homogeneous localization      40
Hook formula      86
Hypersimplex      173
Hypersurface      145
Igusa quartic hypersurface      181
Inflection point      56
Invariant function      1
Isogeneous      42
Isotropy subgroup      98
Jacobian      69
Kempf-stable      141
Laplace formula      19
Laurent monomial      73
Lefschetz Theorem      109
Line $G$-bundle      104
Line $G$-effective      127
Linear algebraic groups      37
Linearization      104
Linearization, democratic      169
Linearization, trivial      105
Module of covariants      70
Moment map      142
Multi-degree      8 11
Multi-weight      11
Multihomogeneous      11
Multiisobaric      11
Multiplicity      55 72
Nagata Theorem      41
Nagata’s conjecture      61
Nagata’s counterexample      52
Normal ring      45
Null-cone, $ix$      32 117 120
Observable subgroup      50
Omega-operator      17
One-parameter subgroup of a torus      77
One-parameter subgroup of an algebraic group      129
One-parameter subgroup, adapted      140
One-parameter subgroup, destabilizing      138
One-parameter subgroup, most responsible for instability      140
Order of concomitant      69
Order of contravariant      69
Parabolic subgroup      50
Plethysm decomposition      81
Pluecker equations      24
Polar hypersurface      14
Polarization      5
Polarization map      6
Projective invariant      46
Projective space      39
Projective spectrum      38
Proper map      132
Quadratic form      4
Quantic      87
Quotient, categorical      92
Quotient, geometric      92
Quotient, good categorical      94
Quotient, good geometric      92
Radical      42
Rank      74
Rational action on an algebra      37
Rational character of a torus      73
Rational character of an algebraic group      106
Rational convex polyhedral cone      188
Rational quotient      100
Rational representation      37 73
Reductive algebraic group      42
Regular action      37
Regular function      35
Restitution      5
Resultant      69
Reynolds operator      71
Ring of invariants      2
Ringed space      118
Root      73
Root, dual      77
Root, negative      74
Root, positive      74
Root, simple      74
Schroedinger representation      142
Schur multipliers      108
Segre cubic primal      180
Segre quartic primal      181
Self-association involution      181
Semi-stable      115
Semiinvariant      65
Skeleton      199
Small resolution      126
Solvable algebraic group      42
Stabilizer      41
Stable      115
Stable, properly      116
Straightening law      23
Structure sheaf      118
Symbolic expression      9
Tableau      12
Tableau function      13
Tableau function, homogeneous      13
Tableau, degree      12
Tableau, homogeneous      12
Tableau, rectangular      12
Tableau, standard      22
Ternary cubic      153
Theta group      141
Tits conjecture      140
Toric variety      192
Transvectant      68
Transversal      171
Unitary trick      32
Unstable      115
Valuative criterion of properness      132
Valuative criterion of separatedness      132
Variation of quotients      143
Veronese embedding      121
Veronese map      83 111
Veronese variety      83
Weierstrass equation      154
Weight      30 46 67
Weight in a representation      73
Weight of covariant      67
Weight polytope of a point      136
Weight polytope of the representation      135
Weight set      136
Weight space      135
Weight, dominant      76 78
Weight, fundamental      78
Weighted projective linearization      196
Weighted projective space      39 180
Weitzenboeck’s Theorem      51
Weyl group      138
Young diagram      86
Zariski’s problem      49
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