Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
À l'intérieur du livre
Résultats 1-3 sur 25
Page 43
... ( v ) = k [ X , Y , Z , W ] / ( XW - YZ ) . Let X , Y , Z , W be the residues of X , Y , Z , W in г ( V ) . Then X / Y = Z / W = f ε k ( V ) = f ɛ k ( V ) is defined at P = ( x , y , z , w ) ɛ V if y ... ( V ) = { fε Op ( V AFFINE VARIETIES 43.
... ( v ) = k [ X , Y , Z , W ] / ( XW - YZ ) . Let X , Y , Z , W be the residues of X , Y , Z , W in г ( V ) . Then X / Y = Z / W = f ε k ( V ) = f ɛ k ( V ) is defined at P = ( x , y , z , w ) ɛ V if y ... ( V ) = { fε Op ( V AFFINE VARIETIES 43.
Page 44
... Op ( V ) | f ( P ) = 0 } is called the maximal ideal SO Γε An element fε Op ( V ) of V at P. It is the kernel of the evaluation homo- morphism f — > f ( P ) of Op ( V ) onto k , Op ( V ) / M ( V ) is isomorphic to k . is a unit in Op ...
... Op ( V ) | f ( P ) = 0 } is called the maximal ideal SO Γε An element fε Op ( V ) of V at P. It is the kernel of the evaluation homo- morphism f — > f ( P ) of Op ( V ) onto k , Op ( V ) / M ( V ) is isomorphic to k . is a unit in Op ...
Page 55
... ( V ) . Show that there is a natural homomorphism from Op ( A ) / J Op ( A ) to Op ( V ) / J ' Op ( V ) , to Op ( V ) / J ' Op ( V ) , and that o is an isomorphism . to Op ( V ) . In particular , Op ( A ) / I Op ( A " ) is isomorphic 2-45 ...
... ( V ) . Show that there is a natural homomorphism from Op ( A ) / J Op ( A ) to Op ( V ) / J ' Op ( V ) , to Op ( V ) / J ' Op ( V ) , and that o is an isomorphism . to Op ( V ) . In particular , Op ( A ) / I Op ( A " ) is isomorphic 2-45 ...
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