Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 140
... closed subvariety of an affine variety is also an affine variety . What is more surprising is that an open subvariety of an affine variety may also be affine . PROPOSITION 5. Let V f ɛ г ( V ) , f ‡ 0. Let V subvariety of V. Then ( 1 ) ...
... closed subvariety of an affine variety is also an affine variety . What is more surprising is that an open subvariety of an affine variety may also be affine . PROPOSITION 5. Let V f ɛ г ( V ) , f ‡ 0. Let V subvariety of V. Then ( 1 ) ...
Page 150
... closed subvariety of a curve is 2 Α P ( 5 ) A closed subvariety of A2 ( resp . p2 ) has dimension one if and only if it is an affine ( resp . projective ) plane curve . Proof : ( 1 ) and ( 2 ) follow from the fact that the varieties ...
... closed subvariety of a curve is 2 Α P ( 5 ) A closed subvariety of A2 ( resp . p2 ) has dimension one if and only if it is an affine ( resp . projective ) plane curve . Proof : ( 1 ) and ( 2 ) follow from the fact that the varieties ...
Page 202
... closed ) since f ( x ) : eurove I would contam anther is not const > V is a morphism from a projective we con 8-19 . If f : C curve to a variety V , then f ( c ) is a closed subvariety of V. ( Hint : Consider C ' = closure of f ( C ) in ...
... closed ) since f ( x ) : eurove I would contam anther is not const > V is a morphism from a projective we con 8-19 . If f : C curve to a variety V , then f ( c ) is a closed subvariety of V. ( Hint : Consider C ' = closure of f ( C ) 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