Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 41
... linear subvariety ‡ show that there is an affine change ( b ) If V & , of coordinates T of An ( Hint : use induction ... linear subvariety of dimension 1 , and that a linear subvariety of dimension 1 is the line through any two of its ...
... linear subvariety ‡ show that there is an affine change ( b ) If V & , of coordinates T of An ( Hint : use induction ... linear subvariety of dimension 1 , and that a linear subvariety of dimension 1 is the line through any two of its ...
Page 51
... linear factors . Proof : The first claim follows directly from ( 1 ) and ( 2 ) of the proposition . For the second , write F = YG , where Y doesn't divide G. F = G = επ 7 ( X - λ ) * since k is algebraically closed , so F = * ε yr II ...
... linear factors . Proof : The first claim follows directly from ( 1 ) and ( 2 ) of the proposition . For the second , write F = YG , where Y doesn't divide G. F = G = επ 7 ( X - λ ) * since k is algebraically closed , so F = * ε yr II ...
Page 193
... linear map , and Ker ( ) = L ( D ) , induces a one - to - one linear map 9 : LD + P ) / L ( P ) — P ) / L ( P ) > k which gives the result . ( 2 ) : This follows from Prop . 1 , Cor . 1 , and from Prop . 2 ( 3 ) . = Ρε Χ , and 0 , and ...
... linear map , and Ker ( ) = L ( D ) , induces a one - to - one linear map 9 : LD + P ) / L ( P ) — P ) / L ( P ) > k which gives the result . ( 2 ) : This follows from Prop . 1 , Cor . 1 , and from Prop . 2 ( 3 ) . = Ρε Χ , and 0 , and ...
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