Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 44
... lemma is an immediate consequence of this . A ring satisfying the conditions of the lemma is called a local ring ; the units are those elements not belonging to the maximal ideal . We have seen that Op ( V ) is a local ring , and M ( V ) ...
... lemma is an immediate consequence of this . A ring satisfying the conditions of the lemma is called a local ring ; the units are those elements not belonging to the maximal ideal . We have seen that Op ( V ) is a local ring , and M ( V ) ...
Page 210
... LEMMA . The heart of the then ( D + P ) = & ( D ) . dy D30 then I just with at zeros . poles 4 If ( D ) > 0 , and 4 e ( W - D - P ) # & ( W - D ) , & Proof : Choose C as before with ordinary multiple points , and such that P is a simple ...
... LEMMA . The heart of the then ( D + P ) = & ( D ) . dy D30 then I just with at zeros . poles 4 If ( D ) > 0 , and 4 e ( W - D - P ) # & ( W - D ) , & Proof : Choose C as before with ordinary multiple points , and such that P is a simple ...
Page 211
... Lemma Applying the induction & ( D - P ) = deg ( D - P ) + 1 - g , SO which is ( * ) D ' 2g - 2 This case can only happen if ( Prop . 3 ( 2 ) ) . So we can pick for which ( * ) is false ; i.e. ( * ) D + P is true for all ΡεΧ . l ( W - D ...
... Lemma Applying the induction & ( D - P ) = deg ( D - P ) + 1 - g , SO which is ( * ) D ' 2g - 2 This case can only happen if ( Prop . 3 ( 2 ) ) . So we can pick for which ( * ) is false ; i.e. ( * ) D + P is true for all ΡεΧ . l ( W - D ...
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