Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 66
... tangent to the curve at ( 0,0 ) . Let F be any curve , P = • where Fi We define F = F + F + + F • m m + 1 of degree i , Fn ' Fm 0 . ( 0,0 ) , and write of F at P = m PE F if and only if mp ( F ) > 0 . ( 0,0 ) . Write is a form in k [ X ...
... tangent to the curve at ( 0,0 ) . Let F be any curve , P = • where Fi We define F = F + F + + F • m m + 1 of degree i , Fn ' Fm 0 . ( 0,0 ) , and write of F at P = m PE F if and only if mp ( F ) > 0 . ( 0,0 ) . Write is a form in k [ X ...
Page 67
... F with multiplicity Σ er ́i'i ' ( This is a consequence of the fact that the lowest degree term of F is the product ... tangent lines to F at P , is the multiplicity of the tangent , etc. Note that T takes the points of T tangents to F ...
... F with multiplicity Σ er ́i'i ' ( This is a consequence of the fact that the lowest degree term of F is the product ... tangent lines to F at P , is the multiplicity of the tangent , etc. Note that T takes the points of T tangents to F ...
Page 70
... ( F ) irreducible , show that ( b ) As in ( a ) , is a hypersurface , F Tp ( V ) = { ( V1 , · · · , V2 ) | Σ { ( V1 ... tangent to F at P , then the image of L in Op ( F ) is a uniformizing parameter for Op ( F ) . Proof : Suppose Р is a ...
... ( F ) irreducible , show that ( b ) As in ( a ) , is a hypersurface , F Tp ( V ) = { ( V1 , · · · , V2 ) | Σ { ( V1 ... tangent to F at P , then the image of L in Op ( F ) is a uniformizing parameter for Op ( F ) . Proof : Suppose Р is a ...
Table des matières
Chapter One Affine Algebraic Sets | 1 |
Chapter Two Affine Varieties | 38 |
35 | 51 |
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 denote div(G div(z divisor element F and G F ɛ finite number flex follows form of degree function field Hint hyperplane hypersurface induced integer intersection number isomorphism LEMMA Let F linear local ring maximal ideal module-finite morphism mp(F Noether's non-singular non-zero Nullstellensatz Op(C Op(F 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 resp ring homomorphism simple point subring subvariety Suppose tangent line uniformizing parameter unique vector space zero ε Ι Ρε