Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 36
... F ( a1 , a ) n is called a polynomial function if there is a polynomial F ε k [ X1 ' k [ X1 , ... , X ] such that f ( a , ... , a ) = F ( a ̧ ‚ ......... ‚ a ̧ ) for all ( a , ... , a ) ε V. ɛ The polynomial functions form a subring of ...
... F ( a1 , a ) n is called a polynomial function if there is a polynomial F ε k [ X1 ' k [ X1 , ... , X ] such that f ( a , ... , a ) = F ( a ̧ ‚ ......... ‚ a ̧ ) for all ( a , ... , a ) ε V. ɛ The polynomial functions form a subring of ...
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... polynomial function if there is a polynomial F ε k [ X1 , ... , X ] such that f ( a1 , ... .. ‚ a ̧ ) κ n n = F ( a1 , ... , a ) n for all ( a , ... , an ) a ) ε V. The polynomial functions form a subring of J ( V , k ) containing k . Two ...
... polynomial function if there is a polynomial F ε k [ X1 , ... , X ] such that f ( a1 , ... .. ‚ a ̧ ) κ n n = F ( a1 , ... , a ) n for all ( a , ... , an ) a ) ε V. The polynomial functions form a subring of J ( V , k ) containing k . Two ...
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... F be an irreducible polynomial in k [ X , Y ] , and suppose Let V = V ( F ) n- F is monic in Y : F = y2 + a1 ( X ) y1 - 1 + ...... . 2 A2 . Show that the natural homomorphism ... polynomial map T : A " m AFFINE VARIETIES 37 Polynomial Maps.
... F be an irreducible polynomial in k [ X , Y ] , and suppose Let V = V ( F ) n- F is monic in Y : F = y2 + a1 ( X ) y1 - 1 + ...... . 2 A2 . Show that the natural homomorphism ... polynomial map T : A " m AFFINE VARIETIES 37 Polynomial Maps.
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