Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 154
... birational if there are open sets UC X , VC Y , isomorphism f : U is said to be and an F. We say > V which represents that X and Y are birationally equivalent if there is 154 ALGEBRAIC CURVES.
... birational if there are open sets UC X , VC Y , isomorphism f : U is said to be and an F. We say > V which represents that X and Y are birationally equivalent if there is 154 ALGEBRAIC CURVES.
Page 155
... birationally equivalent if there is a birational map from X to Y ( This is easily seen to be an equivalence relation ) . A variety is birationally equivalent to any open subvariety of itself . An and ph are birationally equivalent . Α ...
... birationally equivalent if there is a birational map from X to Y ( This is easily seen to be an equivalence relation ) . A variety is birationally equivalent to any open subvariety of itself . An and ph are birationally equivalent . Α ...
Page 156
... birationally equivalent to ph + m . Show that p1 x pl is not isomorphic to p2 . ( Hint : 1 1 P 2 Р Р x P has closed subvarieties of dimension one which do not intersect . ) 6-40 . If there is a dominating rational map from X to then dim ...
... birationally equivalent to ph + m . Show that p1 x pl is not isomorphic to p2 . ( Hint : 1 1 P 2 Р Р x P has closed subvarieties of dimension one which do not intersect . ) 6-40 . If there is a dominating rational map from X to then dim ...
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