Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 43
... defined at ɛ P = ( x , y , z , w ) ε V if y0 or w # 0 ( See Problem 2-20 ) . Let Ρεν . We define Op ( V ) to be the set of rational functions on V which are defined at P. It is easy to verify that Op ( V ) forms a subring of k ( V ) kC ...
... defined at ɛ P = ( x , y , z , w ) ε V if y0 or w # 0 ( See Problem 2-20 ) . Let Ρεν . We define Op ( V ) to be the set of rational functions on V which are defined at P. It is easy to verify that Op ( V ) forms a subring of k ( V ) kC ...
Page 86
... defined , but that it is a well - defined notion to say th whether the i -coordinate is zero or non - zero ; and , if x ; ‡ 0 , the ratios X / X ; are well - defined ( since they are unchanged under equivalence ) . n We let U1 = { ( x ...
... defined , but that it is a well - defined notion to say th whether the i -coordinate is zero or non - zero ; and , if x ; ‡ 0 , the ratios X / X ; are well - defined ( since they are unchanged under equivalence ) . n We let U1 = { ( x ...
Page 207
... define the order of at P , ordp ( w ) , as ய Choose a uniformizing parameter = m fdt , f ɛ K , and let ordp ( w ) t that this is well - defined , suppose uniformizing parameter , and fdt = ord ( w ) , as follows : = ( mat alg / k ) in ...
... define the order of at P , ordp ( w ) , as ய Choose a uniformizing parameter = m fdt , f ɛ K , and let ordp ( w ) t that this is well - defined , suppose uniformizing parameter , and fdt = ord ( w ) , as follows : = ( mat alg / k ) in ...
Table des matières
Chapter One Affine Algebraic Sets | 1 |
Chapter Two Affine Varieties | 38 |
35 | 51 |
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 denote div(G div(z divisor element F and G F ɛ finite number flex follows form of degree function field Hint hyperplane hypersurface induced integer intersection number isomorphism LEMMA Let F linear local ring maximal ideal module-finite morphism mp(F Noether's non-singular non-zero Nullstellensatz Op(C Op(F 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 resp ring homomorphism simple point subring subvariety Suppose tangent line uniformizing parameter unique vector space zero ε Ι Ρε