Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
À l'intérieur du livre
Résultats 1-3 sur 23
Page 13
... finite number will always do . Theorem 1. Every algebraic set is the intersection of a finite number of hypersurfaces . n Proof : Let the algebraic set be V ( I ) for some ideal I k [ X1 , ... , x ] . It is enough to show that I is ...
... finite number will always do . Theorem 1. Every algebraic set is the intersection of a finite number of hypersurfaces . n Proof : Let the algebraic set be V ( I ) for some ideal I k [ X1 , ... , x ] . It is enough to show that I is ...
Page 18
... finite number of zeros . This shows that only a finite number of X - coordinates appear among the points of V ( F , G ) . Since the same reasoning applies to the Y - coordinates , there can be only a finite number of points . COROLLARY ...
... finite number of zeros . This shows that only a finite number of X - coordinates appear among the points of V ( F , G ) . Since the same reasoning applies to the Y - coordinates , there can be only a finite number of points . COROLLARY ...
Page 55
... Finite Number of Zeros . The proposition of this section will be used to relate local questions ( in terms of the local rings Op ( V ) ) with global ones ( in terms of coordinate rings ) . PROPOSITION 6. Let I be ... Finite Number of Zeros.
... Finite Number of Zeros . The proposition of this section will be used to relate local questions ( in terms of the local rings Op ( V ) ) with global ones ( in terms of coordinate rings ) . PROPOSITION 6. Let I be ... Finite Number of Zeros.
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