Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
À l'intérieur du livre
Résultats 1-3 sur 79
Page 74
... ( F ) / ( r - 1 ) : . Can you find a definition for the multiplicity of a local ring which makes sense in all the cases you know ? 3. Intersection Numbers Let F and G be plane curves , Ρε Pɛ A2 . We want to define the intersection number of F ...
... ( F ) / ( r - 1 ) : . Can you find a definition for the multiplicity of a local ring which makes sense in all the cases you know ? 3. Intersection Numbers Let F and G be plane curves , Ρε Pɛ A2 . We want to define the intersection number of F ...
Page 75
... F ↑ G ) . = P , then ( 4 ) I ( P , FN G ) = I ( P , GN F ) . Two curves F and G are said to intersect transversally at Р if P is a simple point both on and on G , and if the tangent line to F at P is different from the tangent line to ...
... F ↑ G ) . = P , then ( 4 ) I ( P , FN G ) = I ( P , GN F ) . Two curves F and G are said to intersect transversally at Р if P is a simple point both on and on G , and if the tangent line to F at P is different from the tangent line to ...
Page 77
... F and G pass through P. Let O. = Op ( A2 ) . have no common components , Prop . 6 , Cor . 1. If F H , then ( F , G ) ( H ) , ≤ I ( P , FG ) and G so there If F and G is finite by Chapter 2 , have a common component is a homomorphism from / ...
... F and G pass through P. Let O. = Op ( A2 ) . have no common components , Prop . 6 , Cor . 1. If F H , then ( F , G ) ( H ) , ≤ I ( P , FG ) and G so there If F and G is finite by Chapter 2 , have a common component is a homomorphism from / ...
Table des matières
Chapter One Affine Algebraic Sets | 1 |
Chapter Two Affine Varieties | 38 |
35 | 51 |
Droits d'auteur | |
9 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 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