Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 112
... Bezout's Theorem Show div > 1 The projective plane was constructed so that any two distinct lines would intersect at one point . The famous theorem of Bezout tells us that much more is true : BEZOUT'S THEOREM . Let F and G be projective ...
... Bezout's Theorem Show div > 1 The projective plane was constructed so that any two distinct lines would intersect at one point . The famous theorem of Bezout tells us that much more is true : BEZOUT'S THEOREM . Let F and G be projective ...
Page 115
... Bezout's Theorem , we deduce COROLLARY 1. If F and G have no common component " Em ( F ) m ( G ) ≤ deg ( F ) · deg ( G ) . P COROLLARY 2. If F and G meet in mn distinct points , m = deg ( F ) , n = deg ( G ) , points on F and on G ...
... Bezout's Theorem , we deduce COROLLARY 1. If F and G have no common component " Em ( F ) m ( G ) ≤ deg ( F ) · deg ( G ) . P COROLLARY 2. If F and G meet in mn distinct points , m = deg ( F ) , n = deg ( G ) , points on F and on G ...
Page 211
... Bezout's Theorem , H must contain L as a component . In particular , H ( P ) = 0. Since P does not appear in it follows that D ' + P > P , or D ' > 0 , E + A + B , as desired . We turn to the proof of the theorem . For each divisor D ...
... Bezout's Theorem , H must contain L as a component . In particular , H ( P ) = 0. Since P does not appear in it follows that D ' + P > P , or D ' > 0 , E + A + B , as desired . We turn to the proof of the theorem . For each divisor D ...
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