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Hodge W., Vallance D, Pedoe D. — General theory of algebraic varieties in projective space
Hodge W., Vallance D, Pedoe D. — General theory of algebraic varieties in projective space

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Название: General theory of algebraic varieties in projective space

Авторы: Hodge W., Vallance D, Pedoe D.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 402

Добавлена в каталог: 31.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(\alpha,\beta)$ correspondence      105
$\Omega(d,n)$, complete intersection with primal      368
$\Omega(d,n)$, Grassmann variety of d-spaces in $S_{n}$      310
$\Omega_{a_{0}a_{1}...a_{d}}$, Schubert variety      316
Absolutely irreducible variety      68
Algebraic correspondence      89 100
Algebraic varieties      3
Algebraic varieties, system of      67
Algebraically closed field      74
Associative law of intersection in $S_{n}$      166
Automorphism of extension over field      66
Automorphism of field      66
Base for subvarieties of a quadric      238
Base for subvarieties of Grassmannian      337
Base for varieties      194
Bezout’s Theorem      158
Birational correspondence      105
Birational equivalence      106
Canonical form for cubic ternary form      118
Canonical form for equations of intersection of two quadrics      287
Canonical form for pair of quadrics      278
Canonical form for quadric      204
Carrier-variety of algebraic system      113
Cayley form      33
Cayley form of variety in r-way space      97
Cayley form, algebraic conditions for      51
Cayley image of algebraic system      113
Characters      361
Class of curve and surface      361
Commutative law of intersection in $S_{n}$      159
Complete intersection of $\Omega(d,n)$ and primal      368
Complete intersection of quadric and primal      244
Component, irreducible, of variety      10
Component, redundant      10
Condition for Cayley form      61
Condition for reducibility      6
Cone projecting a variety      46
Conjugate elements      64
Conjugate extensions      64
Conjugate points with regard to a quadric      207
Conjugate set of points      27
Conjugate spaces      218
Continuous system of varieties      180
Coordinates, non-homogenoous      16
Coordinates, normalised      16
Correspondence, algebraic      89 100
Correspondence, birational      105
Correspondence, determined by joining $V_{a}$ to $V_{b}$      164
Correspondence, image-points in      102
Correspondence, irreducible      100
Correspondence, object-points in      102
Correspondence, reducible      100
Cross-join of two varieties      154
Degree of conjugacy      218
Dimension of a variety      23
Dimension of a variety in r-way space      92
Direct product of two varieties      146
Distributive law of intersection in $S_{n}$      160
Dual of quadric      213
Dual of Schubert condition      319
Effective variety      185
Elementary enumerative characters      361
Elements, conjugate      64
Enveloping field      2
Equivalence $(\equiv) $      180
Equivalence $(\equiv) $ in the narrow sense $(\equiv) $      182
Equivalence $(\equiv) $ in the virtual sense $(\sim) $      186
Equivalence $(\equiv) $ in the wide sense      183
Equivalence $(\equiv) $, birational      106
Equivalence $(\equiv) $, classes $[V_{a}]$      184
Equivalent varieties      180
Extensions, conjugate      64
Field, algebraic closure      74
Field, algebraically closed      74
Field, automorphism of      66
Field, enveloping      2
Field, intermediate      66
Field, least normal extension of      68
Field, normal extension of      64
Field, stem      63
Field, universal      2
Function field of a variety      15
Fundamental point of stereographic projection      249
Generic k-space      16
Generic point of a variety      10
Generic variety of irreducible system      67
Grade of a variety      193
Grassmann variety      310
Grassmannian      310
Homogeneous ideal      8
Ideal, homogeneous      8
Ideal, prime      8
Image-points in correspondence      102
Image-variety      102
Integrally closed ring      123
Intermediate field      66
Intersection of $V_{a}$ and $V_{b}$ on $V_{n}$      171
Intersection of multiplicative varieties      158
Intersection of systems of equivalence      191
Intersection of systems of varieties      173
Intersection of two quadrics      286
Intersection of varieties      4
Intersection, an intrinsic concept      179
Intersection, associative law for, in $S_{n}$      165
Intersection, commutative law for, in $S_{n}$      159
Intersection, complete, of $\Omega(d, n)$ and primal      368
Intersection, rational, of two quadrics      302
Intersection-number of two varieties      192
Irreducible algebraic correspondence      100
Irreducible components of a variety      10
Irreducible varieties      6
Irregular points of stereographic projection      249
Isolated solution of set of equations      117
Laws of intersection on $V_{n}$      173
Least normal extension of field      68
Linear spaces on a quadric      225
Minimal base for varieties      194
Minimum function of algebraic element      63
Monoidal representation of variety      63
Multiplicative variety      130
Multiplicity of component      130
Multiplicity of solution      127
Multiplicity, positive      127
Multiplicity, zero      127
Non-contractible representation as sum of varieties      10
Non-homogeneous coordinates of point      16
Non-singular quadric      205
Norm of a variety      61
Normal extension of a field      64
Normal problem      121
Normalised coordinates      16
Object-points in algebraic correspondence      102
Object-variety      102
Order of a variety      41
Order of irreducible primal      48
Orthogonal matrix      258
Parameter of algebraic system      113
Parametric representation of variety      63
Pencil of quadrics      286
Pencil of quadrics, in $S_{n}$ (n=1,2,3)      304
Pieri’s formula      354
Point, generic      10
Point, proper specialisation of      91
Point, simple, of variety      87
Point, singular, of variety      87
Points in algebraic correspondence      100
Points, conjugate set of      27
Points, conjugate, with regard to quadric      207
Polar prime      208
Polar r-ad      221
Polar space      216
Pole of prime      215
Positive multiplicity      127
Postulation of variety      371
Primal      26
Primal, order of      48
Prime      26
Prime, at infinity      16
Prime, ideal      8
Prime, passing through point      22
Prime, polar      208
Prime, pole of      215
Principle of conservation of the number      127
Principle of counting constants      104
Principle of Pluecker — Clebsch      116
Projective characters      361
Proper specialisation      91
Proper specialisation of multiplicative variety      131
Pure variety      61
Quadratic transformation      106
Quadric      204
Quadric of type $\rho$      206
Quadric of type $\rho$, alternative form      212
Quadric, complete intersection with primal      244
Quadric, dual of      213
Quadric, envelope      214
Quadric, non-singular      206
Quadric, touched along linear space      217
Quadrics, pencil of      286
Quotient ring of a point      124
Rational intersection of two quadrics      302
Reducibility condition      6
Reducible algebraic correspondence      100
Reducible varieties      6
Redundant component      10
Regular point of stereographic projection      249
Relatively irreducible variety      68
Ring of equivalence systems      192
Ring, integrally closed      123
Schubert condition $(a_{0},a_{1}...a_{d})$      316
Schubert condition $(a_{0},a_{1}...a_{d})$, dual of      319
Schubert system      316
Schubert varieties of complementary dimension      329
Schubert varieties, $\Omega_{a_{0}a_{1}...a_{d}}$      316
Schubert varieties, $\sigma_{h}$      322
Schubert varieties, representation A for      322
Schubert varieties, representation B for      325
Schubert varieties, special      318
Segre symbol of pencil      289
Segre variety      96
Segre variety, standard power-products for      98
Self-conjugate space      218
Self-polar simplex      209
Simple intersection along a variety      163 170
Simple point of a variety      87
Singular locus of a variety      87
Singular point of a variety      87
Space, independent of a point      166
Special Schubert varieties      318
Specialisation, proper      91
Standard power-products      377
Standard power-products for Segre variety      98
Stem field      63
Stereographic projection      247
Stereographic projection, irregular points of      249
Sum of varieties      4
System from projective transformation      142
System of all k-spaces in $S_{n}$      18
System of all k-spaces through a given space      19
System of equivalence {$V_{a}$}      187
System of equivalence {$V_{a}\cdotV_{b}$}={$V_{a}$}$\cdot${$V_{b}$}      189
System of orthogonal matrices      265
System of varieties      67
Tableau      377
Tangent space to variety      88
Universal field      2
Unmixed variety      61
Varieties, continuous system of      180
Varieties, cross-join of two      154
Varieties, direct product of two      146
Varieties, equivalent      180
Varieties, intersecting simply along a variety      163 170
Varieties, intersections of multiplicative      168
Varieties, non-contractible representation of variety as sum of      10
Varieties, sum of      4
Variety in r-way space      89
Variety of order one      48
Variety, absolutely irreducible      68
Variety, algebraic      3
Variety, component      9
Variety, cone projecting a      46
Variety, contained in another      5
Variety, degenerated into two varieties      146
Variety, dimension in r-way space      92
Variety, dimension of      23
Variety, effective      185
Variety, function field of      16
Variety, generic point of      10
Variety, grade of      193
Variety, Grassmann      310
Variety, image-      102
Variety, irreducible      6
Variety, irreducible component of      10
Variety, lying in another variety      6
Variety, monoidal representation of      63
Variety, multiplicative      130
Variety, non-singular      170
Variety, norm of      61
Variety, object-      102
Variety, order of      41
Variety, order, characteristic property of      61
Variety, parametric representation of      63
Variety, postulation of      371
Variety, pure      61
Variety, reducible      6
Variety, relatively irreducible      68
Variety, Schubert      316
Variety, Segre      95
Variety, singular locus of      87
Variety, tangent space to      88
Variety, unmixed      51
Vertex of quadric      207
Virtual variety      184
Z-space      155
Zero multiplicity      127
Zero variety      185
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