Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 43
... f is defined at P if and only if b ( P ) # 0 . = Example . V V ( XW - YZ ) C Aa ( k ) . г ( 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 ...
... f is defined at P if and only if b ( P ) # 0 . = Example . V V ( XW - YZ ) C Aa ( k ) . г ( 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 ...
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An Introduction to Algebraic Geometry William Fulton, Richard Weiss. 3.16 . Let F ɛ k [ X1 , X ] define a hypersurface in A. r Write F = F + F + ... and let m = m m + 1 " m ( F ) where P = ( 0,0 ) . Suppose F is irreducible , and let O = Op ...
An Introduction to Algebraic Geometry William Fulton, Richard Weiss. 3.16 . Let F ɛ k [ X1 , X ] define a hypersurface in A. r Write F = F + F + ... and let m = m m + 1 " m ( F ) where P = ( 0,0 ) . Suppose F is irreducible , and let O = Op ...
Page 106
... Let P be a simple point on tangent line to F at F. Show that the P is F ( P ) X + Fy ( P ) Y + F2 ( P ) Z = 0 . 5-5 * . Let P = ( 0,1,0 ) , F a curve of degree n , i i ་ F = [ F ; ( X , Z ) y1 - i , F. a form of degree i . Show that mp ( F ) ...
... Let P be a simple point on tangent line to F at F. Show that the P is F ( P ) X + Fy ( P ) Y + F2 ( P ) Z = 0 . 5-5 * . Let P = ( 0,1,0 ) , F a curve of degree n , i i ་ F = [ F ; ( X , Z ) y1 - i , F. a form of degree i . Show that mp ( F ) ...
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