Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 74
... ( F ) / ( r - 1 ) : . • Can you find a definition for the multiplicity of a local ring which makes sense in all the cases you know ? 3. Intersection Numbers Let F and G be plane curves , P & A2 . We want to define the intersection number of F ...
... ( F ) / ( r - 1 ) : . • Can you find a definition for the multiplicity of a local ring which makes sense in all the cases you know ? 3. Intersection Numbers Let F and G be plane curves , P & A2 . We want to define the intersection number of F ...
Page 75
... G ʼn F ) . F Two curves F and G are said to intersect transversally at P if P is a simple point both on and on G , and if the tangent line to F at Р is different from the tangent line to G at P. We want the intersection number to be one ...
... G ʼn F ) . F Two curves F and G are said to intersect transversally at P if P is a simple point both on and on G , and if the tangent line to F at Р is different from the tangent line to G at P. We want the intersection number to be one ...
Page 77
... F and pass through P. Let σ = Op ( A2 ) . G If F and G have no common components , Prop . 6 , Cor . 1. If F and G I ( P , FG ) H , then ( F , G ) ( H ) , < so there is finite by Chapter 2 , have a common component is a homomorphism from / ( ...
... F and pass through P. Let σ = Op ( A2 ) . G If F and G have no common components , Prop . 6 , Cor . 1. If F and G I ( P , FG ) H , then ( F , G ) ( H ) , < so there is finite by Chapter 2 , have a common component is a homomorphism from / ( ...
Table des matières
Chapter One Affine Algebraic Sets 1 Algebraic Preliminaries | 1 |
Affine Space and Algebraic Sets | 7 |
The Ideal of a Set of Points | 10 |
Droits d'auteur | |
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Expressions et termes fréquents
affine variety algebraic set algebraic subset algebraically closed assume Bezout's Theorem birational birationally equivalent called change of coordinates Chapter closed subvariety comaximal COROLLARY curve F curve of degree defined deg(D deg(F denote div(G div(z divisor element F and G f ɛ finite number follows form of degree function field Hint homogeneous hyperplane hypersurface induced integer intersection number isomorphism k[X₁ LEMMA Let F linear local ring maximal ideal module-finite morphism mp(F Noether's non-singular non-zero Nullstellensatz Op(C Op(V open subvariety ordinary multiple points plane curve point on F polynomial map Problem projective change projective curve projective plane curve projective variety Proof Prop PROPOSITION quadratic transformation quotient field R-module rational function residue ring homomorphism simple point subring subvariety Suppose tangent line uniformizing parameter unique V₁ vector space Xn+1 zero Ρε