Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 72
... ( Problem 2-49 ( e ) and Chapter 2 , Prop . 7 ) . We may assume that P = ( 0,0 ) , So Mn = I , where I = ( X , Y ) = k [ X , Y ] ( Problem 2-43 ) . Since V ( I ) = { P } , 2 * [ X , Y ] / ( I " , ) = ✪p ( A2 ) / ( 1o , F ) p ( A2 ) = op ...
... ( Problem 2-49 ( e ) and Chapter 2 , Prop . 7 ) . We may assume that P = ( 0,0 ) , So Mn = I , where I = ( X , Y ) = k [ X , Y ] ( Problem 2-43 ) . Since V ( I ) = { P } , 2 * [ X , Y ] / ( I " , ) = ✪p ( A2 ) / ( 1o , F ) p ( A2 ) = op ...
Page 185
... ( Problem 7-14 ) . 7-22 . Let Р be a node on an irreducible plane curve and let L1 , L2 be the tangents to F at P. F ... Problem 5-23 ) . ( b ) If P is a cusp on F , show that I ( P , F H ) = 8. ( See Problem 7-6 ) . ( c ) Use ( a ) and ...
... ( Problem 7-14 ) . 7-22 . Let Р be a node on an irreducible plane curve and let L1 , L2 be the tangents to F at P. F ... Problem 5-23 ) . ( b ) If P is a cusp on F , show that I ( P , F H ) = 8. ( See Problem 7-6 ) . ( c ) Use ( a ) and ...
Page 195
... ( Problem 2-29 ) . It follows that for some div ( w . ) + tZ > 0 , i t > 0 , -j i = 1 , ... , n . Then w1x3 ε L ( ( r ... Problem 8-1 ) . Problems . 8-8 * . If DD ' , ( D ' ) ≤ l ( D ) + deg ( D ' - D ) , 8-9 . Let X = p1 , t L ( r ( t ) ...
... ( Problem 2-29 ) . It follows that for some div ( w . ) + tZ > 0 , i t > 0 , -j i = 1 , ... , n . Then w1x3 ε L ( ( r ... Problem 8-1 ) . Problems . 8-8 * . If DD ' , ( D ' ) ≤ l ( D ) + deg ( D ' - D ) , 8-9 . Let X = p1 , t L ( r ( t ) ...
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
Autres éditions - Tout afficher
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