Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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... degree d , write f = f + f . f ε R [ X1 n where f is a form of degree i R [ X1 , ... , xn + 1 ] by setting d ... + fa = X f ( X1 / Xn + l ' • n + 1 .... * f = fo + f1 .. f * · i , and define f ε xd Xn + 1 fo X / Xn + 1 ) n ' f xd - l f ...
... degree d , write f = f + f . f ε R [ X1 n where f is a form of degree i R [ X1 , ... , xn + 1 ] by setting d ... + fa = X f ( X1 / Xn + l ' • n + 1 .... * f = fo + f1 .. f * · i , and define f ε xd Xn + 1 fo X / Xn + 1 ) n ' f xd - l f ...
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... form of degree d if there is a form F of degree d in k [ X1 , ... , xn + 1 ] whose residue is f . PROPOSITION 2. Every element f ɛ [ may be written uniquely as f = f + ... + f f a form of degree i . m ' О ɛ * n + 1 · Proof : If f is the ...
... form of degree d if there is a form F of degree d in k [ X1 , ... , xn + 1 ] whose residue is f . PROPOSITION 2. Every element f ɛ [ may be written uniquely as f = f + ... + f f a form of degree i . m ' О ɛ * n + 1 · Proof : If f is the ...
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... forms of degree d in form a finite - dimensional vector space over k . 4-10 . Let R = k [ X , Y , Z ] , F & R an irreducible form of 2 In ( V ) . degree n , V = C = V ( F ) ≤ P2 , I = г2 ( V ) . h ( a ) Construct an exact sequence О ...
... forms of degree d in form a finite - dimensional vector space over k . 4-10 . Let R = k [ X , Y , Z ] , F & R an irreducible form of 2 In ( V ) . degree n , V = C = V ( F ) ≤ P2 , I = г2 ( V ) . h ( a ) Construct an exact sequence О ...
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