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| Walker R.J. — Algebraic Curves |
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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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