Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 41
... change of coordinates on of An ( k ) . n T A , then V is also a linear subvariety ‡ show that there is an affine change ( b ) If V & , of coordinates T of An ( Hint : use induction on such that VT = V ( Xm + 1 · · · , Xn ) . r ) . ( c ) ...
... change of coordinates on of An ( k ) . n T A , then V is also a linear subvariety ‡ show that there is an affine change ( b ) If V & , of coordinates T of An ( Hint : use induction on such that VT = V ( Xm + 1 · · · , Xn ) . r ) . ( c ) ...
Page 95
... change of coordinates T : P2 that T ( P ) = Q¡ , i = 1,2,3 . * 4-15 Show that any two distinct lines in P in one point . 2 such intersect 4-16 * . Let L , L , L ̧ ( resp . M1 , M , M ) be lines in p2 ( k ) 2 ' which do not all pass ...
... change of coordinates T : P2 that T ( P ) = Q¡ , i = 1,2,3 . * 4-15 Show that any two distinct lines in P in one point . 2 such intersect 4-16 * . Let L , L , L ̧ ( resp . M1 , M , M ) be lines in p2 ( k ) 2 ' which do not all pass ...
Page 169
... coordinates Τ of P f..T f ' . a projective change of coordinates then there is a projective change of such that T ( P ) = Pi and f1 • T = T1of2 ( See Problem 7-8 below ) . i i i ( 5 ) We want to study π in a neighborhood of a point Q in ...
... coordinates Τ of P f..T f ' . a projective change of coordinates then there is a projective change of such that T ( P ) = Pi and f1 • T = T1of2 ( See Problem 7-8 below ) . i i i ( 5 ) We want to study π in a neighborhood of a point Q in ...
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 | |
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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