Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 80
... proof of the lemma , and also of Theorem 3 . Two things should be noticed about the uniqueness part of the above proof . First , it shows that , as axioms , Properties ( 1 ) - ( 7 ) are exceedingly redundant ; for example , the only ...
... proof of the lemma , and also of Theorem 3 . Two things should be noticed about the uniqueness part of the above proof . First , it shows that , as axioms , Properties ( 1 ) - ( 7 ) are exceedingly redundant ; for example , the only ...
Page 123
... Proof : Let C be three sides , C ' the three the conic , and apply Proposition 2 . opposite sides , Q COROLLARY 2 ... Proof : The two lines form a conic , and the proof is the the same as in Cor . 1 . Pascal's Theorem Pappas ' Theorem ...
... Proof : Let C be three sides , C ' the three the conic , and apply Proposition 2 . opposite sides , Q COROLLARY 2 ... Proof : The two lines form a conic , and the proof is the the same as in Cor . 1 . Pascal's Theorem Pappas ' Theorem ...
Page 140
... proof is complete . Note : It is possible to define more general varieties than those we have considered here . If this were done , the varieties we have defined would be called the " quasi- projective " varieties . A closed subvariety ...
... proof is complete . Note : It is possible to define more general varieties than those we have considered here . If this were done , the varieties we have defined would be called the " quasi- projective " varieties . A closed subvariety ...
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