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| Fulton W. — Algebraic curves |
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| Предметный указатель |
Adjoint 190
Affine n-space 7
Affine n-space, algebraic set 8
Affine n-space, change of coordinates 40
Affine n-space, line 7
Affine n-space, plane 7
Affine n-space, plane curve 8 63
Affine n-space, variety 34 138
Algebraic set 9
Algebraic set, group 174-178
Algebraic set, transform 172
Algebraic set, variety 135
Bezout's theorem 112
Bidegree, biform, bihomogeneous 100
Birational equivalence 155
Blowing'up a point 162
Canonical divisor 207
Clifford's theorem 212
conic 103
Coordinate hyperplane, axes 91
Coordinate hyperplane, ring 34
Cremena transformation 172
Cubic 103
Cubic, addition on 124
Curve 150
Cusp 82
Defined at a point 42 93
Degree of a curve 63 103
Degree of a curve, of a divisor 187
Degree of a curve, of a morphism 214
Degree of a curve, of a zero-cycle 119
Diagonal 146
Differential on a curve 207
Differential on a curve, of the first kind 212
DIMENSION 41 95 150
Discrete valuation ring 47
Divisor 187
Divisor, degree of 187
Divisor, effective 187
Divisor, linear equivalence of 189
Divisor, of a curve 188
Divisor, of a differential 207
Divisor, of a function 188
Divisor, of zeros 188
Dominate a local ring 153
Dominating rational map 153
Double point 66
Dual curve 158
Duality 96
Exact 58
Excellent position 175
Exceptional line 172
Flex 73
FORM 92
Function field 92
Function field, algebraic 149
Fundamental point 172
Genus 196
Good position 173-
Graph 39> 1^6
hessian 116
Homogeneous coordinates 86
Homogeneous coordinates, coordinate ring 91
Homogeneous coordinates, function field 92
Homogeneous coordinates, ideal 89
Hurwitz formula 215
Hyperplane 8 91
Hyperplane, at infinity 87 91
Hypersurface 8 91
Ideal of an algebraic set 11
INDEX 212
Intersect properly 74
Intersect properly, transversally 75
Intersection number 74
Irreducible algebraic set 15 90 135
Irreducible algebraic set, components 17 64 90
Jacobian matrix 69
| Line 8 41 63 95
Line, at infinity 87
Linear subvariety 41 94
Linear subvariety, equivalence 189
Linear subvariety, series 214
Linear subvariety, system 108 109
Local ring 44
Local ring, of a field 159
Local ring, of a variety at a point 43 135
Maximal ideal of a variety at a point 44
Morphism 138
Multiple component 64
Multiple component, point 64 159
Multiplicity of a component 64
Multiplicity of a component, of a point 66 104
Multiplicity of a component, of a tangent 66
Multiprojective space 100 101
Multispace 101
Node 66
Noether's conditions 120
Noether's Fundamental Theorem 120
Noether's Reduction Lemma 210
Noetherian ring 13
Nonsingular curve 64 159
Nonsingular curve, model 180
Nullstellensatz 21
Order 47
Order, function 48
Order, of a differential 207
Order, of a rational function 71
Ordinary multiple point 66 105
Pappus, Pascal 123
Place 181
Pole set 43
Polynomial function 35
Polynomial function, map 37
Power series 49 50
Primitive element, theorem, of 151
Product of algebraic sets 10
Product of algebraic sets, of algebraic varieties 144
Projection map 39
Projective n-space 85
Projective n-space, algebraic set 89
Projective n-space, change of coordinates 93
Projective n-space, closure 98
Projective n-space, equivalence 105
Projective n-space, line 87
Projective n-space, plane 87
Projective n-space, variety 90 138
Quadratic transformation 171 177
Quadratic transformation, centered at a point 177
Radical of an ideal 11
Ramification 214 215
Rational function 142 93 135
Rational map 153
Rational map, domain of 153
Rational over a field 128
Rational variety 155
Reciprocity theorem of Brill — Noether 213
Residue theorem 190
Riemann — Roch theorem 210
Riemann's theorem 196
Segre imbedding 102
Simple component 64
Simple component, node 185
Simple component, point 64 159
Subvariety 35 135
Tangent line 64 67 105
Tangent line, space 69
Transcendence degree 149
Triple point 66
Uniformizing parameter 47
Value of a function 43 93
Variety 135
Weierstrass point 215
Zariski topology 132 135
Zero-cycle 119
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