Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 91
... hyperplane is a hypersurface defined by a form of degree one . The hyperplanes V ( X ; ) , i = 1 , ... , n + 1 , may be called the coordinate hyperplanes , or the hyperplanes at infinity 2 , the V ( X ; ) with respect to U If n = · i ...
... hyperplane is a hypersurface defined by a form of degree one . The hyperplanes V ( X ; ) , i = 1 , ... , n + 1 , may be called the coordinate hyperplanes , or the hyperplanes at infinity 2 , the V ( X ; ) with respect to U If n = · i ...
Page 96
... hyper- plane ; if H is a hyperplane , point . H * denotes the corresponding ( b ) Show that P ** = P , H ** = H. Show that Ρε Η if and only if H * ɛ P * . 3 . This is the well - known duality of projective space . Affine and Projective ...
... hyper- plane ; if H is a hyperplane , point . H * denotes the corresponding ( b ) Show that P ** = P , H ** = H. Show that Ρε Η if and only if H * ɛ P * . 3 . This is the well - known duality of projective space . Affine and Projective ...
Page 225
... hyperplane , axes , 91 ; ring , 34 . Cremena transformation , 172 . cubic , 103 ; addition on , 124 . curve , 150 . cusp , 82 . defined at a point , 42 , 93 . degree of a curve , 63 , 103 ; of a divisor , 187 ; of a zero - cycle , 119 ...
... hyperplane , axes , 91 ; ring , 34 . Cremena transformation , 172 . cubic , 103 ; addition on , 124 . curve , 150 . cusp , 82 . defined at a point , 42 , 93 . degree of a curve , 63 , 103 ; of a divisor , 187 ; of a zero - cycle , 119 ...
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