Tevelev E. — Projectively dual varieties :: Электронная библиотека попечительского совета мехмата МГУ

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Tevelev E. — Projectively dual varieties

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Название: Projectively dual varieties

Автор: Tevelev E.

Аннотация:

During several centuries various reincarnations of projective duality have inspired research in algebraic and differential geometry, classical mechanics, invariant theory, combinatorics, etc. On the other hand, projective duality is simply the systematic way of recovering the projective variety from the set
of its tangent hyperplanes. In this survey we have tried to collect together
different aspects of projective duality and points of view on it. We hope, that
the exposition is quite informal and requires only a standard knowledge of
algebraic geometry and algebraic (or Lie) groups theory. Some chapters are,
however, more difficult and use the modern intersection theory and homology
algebra. But even in these cases we have tried to give simple examples and
avoid technical difficulties.

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 189

Добавлена в каталог: 14.03.2005

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Предметный указатель

$\mathbb{P}^d$ -bundle      142
$\mathbb{Q}$ -divisors      135
$\mu$ -number      123
1-Cycle      134
Adjoint variety      29
Admissible collection      46
Albert algebra      26 39
ample      16
Ample vector bundle      51
Ampleness      52
Annihilator      1 154
Associated hypersurfaces      88
Base-point free      16
Based exact complex      46
Beilinson spectral sequence      95
Bigraded complex      50
Bitangent      10
Borel subgroup      21
Borel — Weyl — Bott theorem      22
Boundary format      110
Bourbaki numbering      21
Cartan lemma      99
Cartier divisor      15
Caustic      9
Cayley determinant      43
Cayley numbers      26
Cayley trick      53 88
Character group      21
Characteristic of a nilpotent      64
Chern class      105
Chern polynomial      106
Chow forms      89
Class formula      107 122
Class of a plane curve      10
Classical discriminant      23 48 108 118
Classical resultant      53
Clifford algebra      25
Cohomology of Koszul complexes      42
Complete linear system      16
Cone of effective 1-cycles      134
Conical action      30
Conical orbit      30
Conormal bundle      4
Conormal variety      2
Contact locus      7 89
Contact scheme      129
Contraction Theorem      135
Correspondence of branches      10
Cotangent bundle      4
Cusp      10
Cuspidal point      10
Darboux frame      98
Defect of a projective variety      3
Defect of smooth divisors      17
Degeneracy locus      176
Degree of a cycle      105
Del Pezzo fibration      142
Desingularization of a dual variety      6
Determinant of a complex      45
Determinant of a supervector space      43
Determinant of a vector space      43
Discriminant      3
Discriminant complex      46
Discriminant of a binary form      3
Discriminant of a linear operator      27
Discriminant of an element in a Lie algebra      28
Discriminant spectral sequence      49
Dominant weight      21
Doublings of linear systems      173
Dual of the curve      7
Dual of the smooth surface      92
Dual plane curve      8
Dual projective subspace      1
Dual quiver      32
Dual variety      2
Dual variety of a complete intersection      52
Dual variety of a curve      48
Dual variety of a smooth complete intersection      106
Dual vector space      1
Effective 1-cycle      134
Effective divisor      15
Ein Theorems      89
Embedded projective tangent space      2
Euler characteristic      119
Extremal rational curve      135
Extremal ray      135
Fano variety      137
Fermat curve      8
First jet      41
Flex      10
Frobenius integrability condition      98
Fulton — Hansen connectedness theorem      71
Fundamental form      97
Fundamental forms of flag varieties      104
Fundamental weights      21 144
Gauss image      77
Gauss map      96
Grassmanian      23
Grassmanian fibration      88
Group of norm similarities      39
Half-spinor representation      25
Hartshorne conjecture      78 170
Height of a nilpotent orbit      64
Hessian matrix      81
Higher fundamental forms      103
Hilbert polynomial      119
Hilbert scheme      91
Homogeneous $\mathfrak{s}\mathfrak{l}_2$ -triple      62
Homogeneous coordinates      1
Homogeneous real hypersurface      170
Horizontal 1-form      98
Hyperdeterminants      87 110 130
Hyperdeterminants, existence of      87
Hyperplane      1
Index of a Fano variety      137
Inflection point      10
Intersection product      134
Isotropic Grassmanian      24
Isotropic subspace      24
Jacobian ideal      122
Jet bundle      41
Join      75
Jordan algebra      26
Jordan decomposition      154
Katz dimension formula      81
Katz — Kleiman — Holme formula      106
Killing form      21
Kleiman Criterion      135
Kobayashi — Ochiai characterisation      142
Kodaira dimension      92

Kostant partition function      32
Koszul complex      42
Kronecker — Weierstrass theory      174
Lagrangian variety      5
Landman formula      107
Legendre transformation      9
Length of extremal rays      136
Levi subgroup      31
Linear system of divisors      16
Linear systems of bounded rank      172
Linear systems of constant rank      172
Linear systems of quadrics      172
Linear systems of rank bounded below      172
Linearly equivalent divisors      15
Linearly normal variety      14
Lines on flag varieties      104
Local equations of a divisor      15
Lower canonical string      36
Matrix format      130
Matsumura — Monsky theorem      151
Maurer — Cartan equations      98
Maurer — Cartan forms      98
Maximal parabolic subgroup      22
Maximal torus      21
Meusnier — Euler theorem      99
Milnor class      123
Milnor number      123
Moment map      31
Monotonicity theorem      95
Moore — Penrose inverse      61
Mori Cone Theorem      135
Moving frames      98
Mukai fibration      142
Multiple tangent      10
Multiplicities of the discriminant      124
Multisegment      32
Multisegment duality      32
Nef divisors      135
Nef value      136
Nef value morphism      136
Negative roots      21
Neron — Severi group      134
Non-degenerate variety      14
Norm similarities      26
Normal bundle      4
Numerically equivalent      134
Numerically trivial      134
Octonions      26
Ordinary double point      10
Osculating sequence      99
Osculating space      99 103
Parabolic subgroup      22
Parity theorem      91 129
Partial order on the weight lattice      22
Pencils of symmetric matrices      174
Permanent      109
Picard number      134
Pluecker embedding      23 102
Pluecker formulas      10
Polarized variety      17 116 133
Positive roots      21
Product theorem      84
Projection from a subspace      12
Projective second fundamental form      97
Projective subspace      1
Properties of jet bundles      41
Pyasetskii Theorem      30
Quadratic nilpotent      153
Quadric fibration      142
Quasi-annihilator      154
Quasiderivation      155
Quotient projective space      12
Ranks of a projective variety      108
Rationality theorem      136
Reflexivity Theorem      4
Regular algebra      154
Reidermeister torsion      43
Relative secant variety      75
Relative tangential variety      75
Representations of quivers      32
Resultant variety      52
Richardson Lemma      31
Root lattice      144
Ruled variety      7
Schlaeffli formula      11
SCROLL      142
Secant variety      74
Segre class      106
Segre embedding      74 84 101
Segre theorem      83
Self-dual variety      168
Semi-ample divisor      133
Severi variety      27 78 79 102
Short grading      34
Simple roots      21
Singular locus of hyperdeterminants      130
Singular locus of the dual variety      130
Singular scheme      122
Singular subalgebra      153
Smoothness principle      97
Spectral sequence of the double complex      49
Spinor variety      24 102
Stable point      151
Stably twisted discriminant complex      47
Standard projective space      1
Strictly dominant weight      21
Supervector space      43
Sylvester formula      48
Symplectic structure      5
Symplectic structure on the cotangent bundle      5
Symplectic variety      5
Tangent bundle      4
Tangent hyperplane      2
Tangent star      75
Tangential variety      74
Terracini lemma      75
Uniform vector bundle      90 174
Upper canonical string      37
Varieties with small dual varieties      142
Variety of complexes      67
Veronese curve      3
Veronese embedding      23 102
Very ample      16
Very ample vector bundle      52
Weight lattice      21
Weight of a multisegment      32
Weyman's bigraded complex      50
Zak's theorem on linear normality      77
Zak's theorem on Severi varieties      78
Zak's theorem on tangencies      76
Zelevinsky involution      32

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