Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
À l'intérieur du livre
Résultats 1-3 sur 21
Page 66
... tangent line to Р etc. Fm is called a double point , if m = F Р is a simple and in this case at P. If m = 2 3 , a triple point , Since F is a form in two variables , we can write ri m i where the L2 are distinct lines ( Chapter 2 , The ...
... tangent line to Р etc. Fm is called a double point , if m = F Р is a simple and in this case at P. If m = 2 3 , a triple point , Since F is a form in two variables , we can write ri m i where the L2 are distinct lines ( Chapter 2 , The ...
Page 67
... tangent lines to F at P , and ri is the multiplicity of the tangent , etc. Note that T T takes the points of F to ... line to a simple point coincide . Problems . 3-1 . Prove that in the above example P = ( 0,0 ) is the only multiple point on ...
... tangent lines to F at P , and ri is the multiplicity of the tangent , etc. Note that T T takes the points of F to ... line to a simple point coincide . Problems . 3-1 . Prove that in the above example P = ( 0,0 ) is the only multiple point on ...
Page 75
... tangent line to F at Р is different from the tangent line to G at P. We want the intersection number to be one exactly when F and G meet transversally at P. More generally , we require ( 5 ) I ( P , FG ) ≥ mp ( F ) mp ( G ) , with ...
... tangent line to F at Р is different from the tangent line to G at P. We want the intersection number to be one exactly when F and G meet transversally at P. More generally , we require ( 5 ) I ( P , FG ) ≥ mp ( F ) mp ( G ) , with ...
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