Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 43
... defined at P = ( x , y , z , w ) ɛ V if y # 0 or w0 ( See Problem 2-20 ) . Let Ρεν . We define Op ( V ) to be the set of rational functions on V which are defined at P. easy to verify that ( V ) forms a subring of k ( V ) containing ( V ) ...
... defined at P = ( x , y , z , w ) ɛ V if y # 0 or w0 ( See Problem 2-20 ) . Let Ρεν . We define Op ( V ) to be the set of rational functions on V which are defined at P. easy to verify that ( V ) forms a subring of k ( V ) containing ( V ) ...
Page 86
... defined , but that it is a well - defined notion to say whether the i - coordinate is zero or non - zero ; and , if th x ; ‡ 0 , the ratios X / X ; x . are well - defined ( since they i are unchanged under equivalence ) . Ρευ . i We let ...
... defined , but that it is a well - defined notion to say whether the i - coordinate is zero or non - zero ; and , if th x ; ‡ 0 , the ratios X / X ; x . are well - defined ( since they i are unchanged under equivalence ) . Ρευ . i We let ...
Page 207
... defined to be Σ ord ( w ) P . In Prop . 8 we shall show PEX # that only finitely many ordp ( w ) 0 for a given w , so that div ( w ) is a well - defined divisor . Let W = div ( w ) . W is called a canonical divisor . If w ' is another ...
... defined to be Σ ord ( w ) P . In Prop . 8 we shall show PEX # that only finitely many ordp ( w ) 0 for a given w , so that div ( w ) is a well - defined divisor . Let W = div ( w ) . W is called a canonical divisor . If w ' is another ...
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