Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 145
... morphisms . - > X , g : 2 - > Y are morphisms , ( 2 ) If f : Z then ( f , g ) : Z - > X x Y defined by ( f , g ) ( z ) = ( f ( z ) , g ( z ) ) is a morphism . ( 3 ) If f : X ' X , g : Y ' Y are morphisms , then fx g : X ' x Y ' X x Y ...
... morphisms . - > X , g : 2 - > Y are morphisms , ( 2 ) If f : Z then ( f , g ) : Z - > X x Y defined by ( f , g ) ( z ) = ( f ( z ) , g ( z ) ) is a morphism . ( 3 ) If f : X ' X , g : Y ' Y are morphisms , then fx g : X ' x Y ' X x Y ...
Page 153
... morphism belonging - > α α to the equivalence class of the map ; every equivalent f . Thus a rational map morphism is a restriction of from X to Y may also be defined as a morphism f from an open subvariety U of X to Y such that f ...
... morphism belonging - > α α to the equivalence class of the map ; every equivalent f . Thus a rational map morphism is a restriction of from X to Y may also be defined as a morphism f from an open subvariety U of X to Y such that f ...
Page 157
... morphism f : C c ' , Ρε C. Then there C ' a projective plane curve , such that f1 ( f ( P ) ) = { P } . We outline a ... morphism , and = ( P ) = ( 0,0,1 ) . Let C ' be the closure of ( c ) . ( c ) For proper choice of 1 , morphism from ...
... morphism f : C c ' , Ρε C. Then there C ' a projective plane curve , such that f1 ( f ( P ) ) = { P } . We outline a ... morphism , and = ( P ) = ( 0,0,1 ) . Let C ' be the closure of ( c ) . ( c ) For proper choice of 1 , morphism 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 | |
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