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Walker R.J. — Algebraic Curves
Walker R.J. — Algebraic Curves

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Название: Algebraic Curves

Автор: Walker R.J.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 201

Добавлена в каталог: 10.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint      180
Adjoint, special      184
Adjunction      127
Adjunction, algebraic      187—129
Adjunction, transcendental      127
Admissible field      133
Affine space      45—47 51
Algebra      8
Algebraic adjunction      127
Algebraic adjunction, independence      128 131
Algebraic adjunction, transformation      147 196
Algebraically closed field      20 29 50 51 56 98 100
Associate of an element in a domain      14
Associate of an element in a domain, polynomials      28
Axes of affine coordinate system      44
Axiom      5 8
Base point of linear system      63
Basis of one field over another      127
Bezout's theorem      59 111 134 139
Binomial theorem      7
Birational correspondence      134—137
Birational correspondence, branch of a curve      96
Birational correspondence, invariant      170 178 179
Birational correspondence, transformation      135 172 173
Canonical series      178 185 186
Canonical series, curve      188
Center of a parametrization      94
Center of a parametrization of a place      96 137
Center of a parametrization of projection      47
Characteristic of a domain      7 8
Characteristic p      21
Characteristic zero      7 8 20 25 102 130
Class of a curve      115—117 120 153
Class of a place      113 153
Clifford's theorem      186 189
Collineation      48 74
Combination, linear      10
Commutative      6
Complete series      168—170
Complex field      56 58 87 96 102
Component of plane curve      51
Composite series      173 187
Condition, linear      63
Conditional equation      19
Cone      59
Congruence of power series      89—92
conic      63 65 69
Constant      11 32
Coordinates, affine      44
Coordinates, hyperplane      42
Coordinates, protective      32
Correspondence, birational      134—137
Correspondence, one-to-one      4
Cross-ratio      36 36
Cross-ratio of a cubic      193
Cubic curve      64 70—74 120 122—124 165 170 189 191—198
Curve, algebraic      50 61 137 see elliptic etc.
Curves, linear system of      63 162
Cusp      68 83 113 119 153 154
Cusp, ram-phoid      58 86 113
Cut out a cycle      162
CYCLE      161 165 see virtual etc.
Degree of a polynomial      12
Degree of a simple algebraic extension      129 143
Dependence of points      37
Dependence, algebraic      128
Dependence, linear      10
Derivative of a polynomial      21
Derivative of a power series      92
Differential      177 178
Dimension of extension of a field      131 134
Dimension of extension of linear series      164
Dimension of extension of linear sub-space      38 39
Dimension of extension of polynomial ideal      166
Dimension of extension of projective space      34
Discriminant of a polynomial      26
Divisible      7 14
Division transformation      13 16 121
Domain      6
Domain polynomial      11
Domain, homomorphism of      7 8 18
Double point      54
Double point, tangent      154
Drawings, remarks on      56
Dual curves      151—153
Dual curves, spaces      42
Dual curves, sub-spaces      43
Duality      41
Effective cycle      166
Effective cycle, series      166
Element      3
Eliminant      24
Elimination      23
Elliptic curve      187 188 195
Empty set      4
Empty set, dimension of      39
Equality      4
Equation of curve      50
Equation of hyperplane      42
Equation, conditional      19
Equation, linear      11
Equation, root of      19
Equianharmonic cubic      197
Equivalence class      5 9 126 167 168
Equivalence class of coordinate systems      34 39 42 45
Equivalence class of cycles      167
Equivalence class of parametrizations      9
Equivalence class, relation      5 9 125
Euclidean algorithm      16
Euler's theorem      27
EXPONENT      7
Factor      14
Factor, highest common      16 17
Factor, multiple      21 106
Factorization of homogeneous polynomials      28 51
Factorization of polynomials      13—18
Factorization of power series      89
Factorization, unique      14 18
Field      5 7
Field of a curve      132
Fixed point (or place) of a linear series      162
Flex      71 117—120 154
Flex of a cubic      72—74 123 191 193
Formal power series      57—93
FRACTION      7
Frame of reference      37 38
Function      see rational function
Fundamental point      75—86
Fundamental theorem of algebra      20
Genus of a curve      179 185
Geometric property      35
Geometry of a space      35
Ground field      32
Group      6 49 74 167 191 195 197
Harmonic cubic      197
Hessian of a curve      71 117—119
Highest common factor      16 17
Homogeneous polynomial      27—31 50
Homomorphism      4* 126
Homomorphism of a domain      7 8 18
Hypercomplex number system      8
Hyperelliptic curve      187 198
Hyperplane      39
Hyperplane at infinity      44
Hyperplane, coordinates      42
Hypersurface      52 59 66 74 134 137 157
Ideal      125—127
Ideal of a curve      155 156
Ideal, dimension of      156
Image      4
Incident elements      42
Independence      see dependence
Indeterminate      11
Index of specialty      184
Inflection, point of      see flex
Integral domain      see domain
Intersect in a cycle      162
Intersection of curve and line      52
Intersection of curve and line of curves      59 84 108—112
Intersection of curve and line of subspaces      40
Invariant, birational      170 178 179
Inverse      7 10
Involution      49 172
Involution, rational      173
Involution, series compounded of      173
Irreducible curve      50
Irreducible curve, element of a domain      14
Irreducible curve, parametrization      94
Irreducible curve, valuation      158
Irregular line      75—77
Isomorphism      4 8 9 12
Jacobian cycle      177—179
Jacobian cycle, series      180
Join of subspaces      41
Least common multiple      18
Line      36
Line, irregular      75—77
Linear condition      63
Linear condition of points      37
Linear condition, dependence      10
Linear condition, equation      11
Linear condition, place      113
Linear condition, series      162 166 see simple etc.
Linear condition, subspace      38 39 63 167
Linear condition, system of curves      63 162
Linear condition, transformation      48
Lueroth's theorem      151
Map, mapping      4 8
Multiple component      51 108
Multiple component, factor      21 106
Multiple component, least common      18
Multiple component, point      54 113
Multiple component, root      22 105 106
Multiplicity of base point      63
Multiplicity of intersection of two curves      110
Multiplicity of tangent to a curve      117
Multiplicity of two places      115
Negative      5
Neighborhood      82
Neighboring points      74 5#-86
Net of curves      64* 66
Newton polygon      98—105
Node      56 119 153 154
Noether's theorem      120—123 180
Non-singular curve      54
Normal curve      151 174 186
Normal form of a cubic      72
Normal form of a parametrization      95 107 116 153
One-to-one correspondence      4
Order of a curve      52 140 153
Order of a cycle      162
Order of a linear series      163
Order of a place      113 139 153
Order of a polynomial at a place      108
Order of a power series      89 97
Order of a rational function at a place      133
Ordinary multiple point      54
Origin of affine coordinate system      44
Osculating plane      139
Osculating plane, space      139 146
Pappus’ theorem      71
Parallel subspaces      45
Parametrization of plane curve      87 93—96
Parametrization of space curve      137
Pascal's theorem      65
Pencil of curves      64 66
Place of plane curve      96 106—108
Place of space curve      137
Plane      36
Plane, osculating      139
Pluecker formulas      119 120 153 154 180
Pluecker formulas, characteristics      154
Point      32 see singular etc.
Pole of rational function      190
Polynomial      11—31
Power series      57—93
Power series, fractional      97—112
Prime ideal      127 156
Principal ideal      125 128
PRODUCT      5
Projection      47
Projection as rational transformation      145 174
Projectivity      48
Proper subset      3
Protective space      32 34 63 167
Quadratic transformation      74—86
Quadratic transformation as a birational transformation      137
Quartic curve      65 120 154 170 181 182 189
Quotient      9 13
Ramphoid cusp      58 86 113
Rational curve      67—69 81 86 149—151 180 187 190
Rational function      12 127
Rational function on a curve      131—134
Rational function, pole of      190
Rational involution      173
Rational transformation      141—149
Rational transformation and linear series      171
Real field      33 56 87
Reciprocity theorem      186
Reducible curve      51 see
Reduction of singular points      80 81 175
Reduction Theorem      184
Reflexive      4
Remainder      13
Remainder theorem      19
Residue of a linear series      169
Residue theorem      180 181
Residue-class ring      126
Resultant      24 30
Riemann — Roch theorem      185
Riemann's theorem      185
Ring      6 125—127
Ring, residue-class ring      126
Root of an equation      19
Root of an equation, multiple      22 105 106
Salmon's Theorem      194
Satellite line      123 124
Series, fractional      57—112;
Series, linear      162 166; simple etc.
Series, power      57—93
Series, Taylor      22 53
Set      3
Set, empty      4
Sextactic point      124 193
Simple adjunction      127
Simple adjunction, base point of linear system      63
Simple adjunction, point of a curve      64 113
Simple adjunction, series      173
Single-valued transformation      4
Singular point      52 54
Singular point of a space curve      140
Singular point, analysis of      82—84;
Singular point, examples of      56—58
Singular point, reduction of      80 81 175
Space      32
Space, affine      45 51
Space, curve      137—140;
Space, osculating      139 146
Space, projective      32 34 63 167
Spaces, dual      42
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