Relative exactness modulo a polynomial map and algebraic $(\mathbb{C}^p,+)$-actions
| dc.creator | Bonnet, Philippe | |
| dc.date | 2006-02-10 | |
| dc.date.accessioned | 2026-07-07T07:03:18Z | |
| dc.date.available | 2026-07-07T07:03:18Z | |
| dc.description | Let $F=(f_1,...,f_q)$ be a polynomial dominating map from $\mathbb{C}^n$ to $\mathbb{C}^q$. We study the quotient ${\cal{T}}^1(F)$ of polynomial 1-forms that are exact along the fibres of $F$, by 1-forms of type $dR+\sum a_idf_i$, where $R,a_1,...,a_q$ are polynomials. We prove that ${\cal{T}}^1(F)$ is always a torsion $\mathbb{C}[t_1,...,t_q]$-module. The we determine under which conditions on $F$ we have ${\cal{T}}^1(F)=0$. As an application, we study the behaviour of a class of algebraic $(\mathbb{C}^p,+)$-actions on $\mathbb{C}^n$, and determine in particular when these actions are trivial. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/math/0602223 | |
| dc.identifier | http://arxiv.org/abs/math/0602223 | |
| dc.identifier | Bull. Soc. math. France 131 (3), 2003, p. 373-398 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108920 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14R20; 14R25 | |
| dc.title | Relative exactness modulo a polynomial map and algebraic $(\mathbb{C}^p,+)$-actions | |
| dc.type | text |