Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 97
... follows from Chapter 2 , Prop . 5. ( 2 ) is If VC An , I = I ( V ) , then a form F belongs to I * if and only if Εν ε Ι . If I is prime , it follows * readily that I * is also prime , which proves ( 3 ) . To prove ( 5 ) , suppose W is ...
... follows from Chapter 2 , Prop . 5. ( 2 ) is If VC An , I = I ( V ) , then a form F belongs to I * if and only if Εν ε Ι . If I is prime , it follows * readily that I * is also prime , which proves ( 3 ) . To prove ( 5 ) , suppose W is ...
Page 132
... follows : a set WCY is open in Y if there is an open subset U of X such that W = YOU . the For any subset Y of a ... follows : a set UC X is open if X - U is an algebraic subset of X. That this is a topology follows from the properties ...
... follows : a set WCY is open in Y if there is an open subset U of X such that W = YOU . the For any subset Y of a ... follows : a set UC X is open if X - U is an algebraic subset of X. That this is a topology follows from the properties ...
Page 198
... follows from the corollary to Prop . 4 . ( 2 ) g = 1 if and only if C is birationally equivalent to a non - singular cubic ( char ( k ) # 2 ) . For if X is a non - singular cubic , the result follows from Cor . 2 , Problems 8-10 and 5 ...
... follows from the corollary to Prop . 4 . ( 2 ) g = 1 if and only if C is birationally equivalent to a non - singular cubic ( char ( k ) # 2 ) . For if X is a non - singular cubic , the result follows from Cor . 2 , Problems 8-10 and 5 ...
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