Fe b 20 06 Relative exactness modulo a polynomial map and algebraic ( C p , + ) - actions Philippe Bonnet 2 nd February 2008
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چکیده
Relative exactness modulo a polynomial map and algebraic (C p , +)-actions Abstract Let F = (f 1 , .., f q) be a polynomial dominating map from C n to C q. In this paper we study the quotient T 1 (F) of polynomial 1-forms that are exact along the generic fibres of F , by 1-forms of type dR + a i df i , where R, a 1 , .., a q are polynomials. We prove that T 1 (F) is always a torsion C[t 1 , ..., t q ]-module. Then we determine under which conditions on F we have T 1 (F) = 0. As an application, we study the behaviour of a class of algebraic (C p , +)-actions on C n , and determine in particular when these actions are trivial.
منابع مشابه
RELATIVE EXACTNESS MODULO A POLYNOMIAL MAP AND ALGEBRAIC ( C p , + ) - ACTIONS
— Let F = (f1, . . . , fq) be a polynomial dominating map from Cn to Cq. We study the quotient T 1(F ) of polynomial 1-forms that are exact along the generic fibres of F , by 1-forms of type dR+ ∑ aidfi, where R, a1, . . . , aq are polynomials. We prove that T 1(F ) is always a torsion C[t1, . . . , tq ]-module. Then we determine under which conditions on F we have T 1(F ) = 0. As an applicatio...
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