Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
À l'intérieur du livre
Résultats 1-3 sur 10
Page 117
... non - singular cubic has nine flexes , all ordinary . 5-24 . ( a ) Let ( 0,1,0 ) be a flex on an irreducible cubic F , Z = 0 the tangent line to F at ( 0,1,0 ) . ( Char ( k ) = 0 ) . Show that F = ZY2 + byZ + cYXZ + terms in X , Z. Find ...
... non - singular cubic has nine flexes , all ordinary . 5-24 . ( a ) Let ( 0,1,0 ) be a flex on an irreducible cubic F , Z = 0 the tangent line to F at ( 0,1,0 ) . ( Char ( k ) = 0 ) . Show that F = ZY2 + byZ + cYXZ + terms in X , Z. Find ...
Page 128
... non - singular cubic C is rational over ko . Let C ( k ) be the set of points of C which are rational over k 。・( a ) If P , Q & C ( k ) then ( P , Q ) ε C ( k ) . ( b ) If O & C ( k ) , then C ( k ) Ο ε then C ( k ) forms a subgroup ...
... non - singular cubic C is rational over ko . Let C ( k ) be the set of points of C which are rational over k 。・( a ) If P , Q & C ( k ) then ( P , Q ) ε C ( k ) . ( b ) If O & C ( k ) , then C ( k ) Ο ε then C ( k ) forms a subgroup ...
Page 198
... non - singular cubic ( char ( k ) # 2 ) . For if X is a non - singular cubic , the result follows from Cor . 2 , Problems 8-10 and 5-24 ( or Prop . 5 Conversely , if g 1 , then ( P ) ≥ 1 for below ) . all P. l ( rp ) = r By Prop . 3 ...
... non - singular cubic ( char ( k ) # 2 ) . For if X is a non - singular cubic , the result follows from Cor . 2 , Problems 8-10 and 5-24 ( or Prop . 5 Conversely , if g 1 , then ( P ) ≥ 1 for below ) . all P. l ( rp ) = r By Prop . 3 ...
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