Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 140
... open subvariety of an affine variety may also be affine . PROPOSITION 5. Let V f ɛ г ( V ) , f ‡ 0. Let V subvariety of V. Then ( 1 ) 5 ( V ) = be an affine variety , and let = { P ɛ V | f ( P ) ‡ 0 } , an open f ( v ) / f ] = { a / f1 ...
... open subvariety of an affine variety may also be affine . PROPOSITION 5. Let V f ɛ г ( V ) , f ‡ 0. Let V subvariety of V. Then ( 1 ) 5 ( V ) = be an affine variety , and let = { P ɛ V | f ( P ) ‡ 0 } , an open f ( v ) / f ] = { a / f1 ...
Page 153
... open subvarieties are said to be equivalent if their restrictions to U Ո Ս are the same . 1 2 U , NU , Since U12 ... subvariety U of X to Y such that f cannot be extended to a morphism from any larger open subset of X to Y. For any ...
... open subvarieties are said to be equivalent if their restrictions to U Ո Ս are the same . 1 2 U , NU , Since U12 ... subvariety U of X to Y such that f cannot be extended to a morphism from any larger open subset of X to Y. For any ...
Page 155
... open subvariety of itself . An and ph are birationally equivalent . Α PROPOSITION 12. Two varieties are birationally equivalent if and only if their function fields are isomorphic . Proof : Since k ( U ) = k ( X ) for any open ...
... open subvariety of itself . An and ph are birationally equivalent . Α PROPOSITION 12. Two varieties are birationally equivalent if and only if their function fields are isomorphic . Proof : Since k ( U ) = k ( X ) for any open ...
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 | |
26 autres sections non affichées
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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