Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 132
... induced topology on Y is defined as 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 topological space X , closure of Y in X is the intersection of all closed subset of X ...
... induced topology on Y is defined as 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 topological space X , closure of Y in X is the intersection of all closed subset of X ...
Page 154
... induced map f : г ( v ) ( U ) is one - to - one , so ř extends to a one - to - one homomorphism from k ( Y ) = k ( V ) into k ( X ) = k ( U ) . This homomorphism is independent of the choice of f , and is denoted by F. ( 2 ) If P ...
... induced map f : г ( v ) ( U ) is one - to - one , so ř extends to a one - to - one homomorphism from k ( Y ) = k ( V ) into k ( X ) = k ( U ) . This homomorphism is independent of the choice of f , and is denoted by F. ( 2 ) If P ...
Page 211
... induction on ( D ) . Choose Р so that ( D - P ) = & ( D ) -1 ( Problem 8-13 ) . If were false , l ( D - P ) > 0 ... induction deg ( D - P ) + 1 - g , SO which is ( * ) . This case can only happen if ( Prop . 3 ( 2 ) ) . So we can pick a ...
... induction on ( D ) . Choose Р so that ( D - P ) = & ( D ) -1 ( Problem 8-13 ) . If were false , l ( D - P ) > 0 ... induction deg ( D - P ) + 1 - g , SO which is ( * ) . This case can only happen if ( Prop . 3 ( 2 ) ) . So we can pick a ...
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