Ga actions on c3 and c7

“…We end these recalls with the factorial closedness property, which is essential for rings of invariants (see [4], [5]). This implies deg D (P ) = 0, and P is invariant with respect to D.…”

Section: If ϕ Is Generated By D Then C[x]mentioning

confidence: 99%

Relative exactness modulo a polynomial map and algebraic $(\mathbb{C}^p , +)$-actions

Bonnet¹

2003

Bul. Soc. Math. France

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Abstract. -Let F = (f 1 , . . . , fq) be a polynomial dominating map from C n to C q . 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 , . . . , aq are polynomials. We prove that T 1 (F ) is always a torsion C[t 1 , . . . , tq]-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.

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“…In fact this is strongly related to Hilbert's fourteenth problem. We refer to [7], [11], and [6] for more details.…”

Section: Proposition 24 Let D Be a Locally Nilpotent Derivation On mentioning

confidence: 99%

“…Locally nilpotent derivations have shown to be very useful in the study of various problems in algebra, algebraic geometry, and differential equations (see [6], [7], [11], [16], [1], [17], [18], [8], [9], and [10]). …”

Section: Introductionmentioning

confidence: 99%