Mixed Hodge structure of affine hypersurfaces
| dc.creator | Movasati, Hossein | |
| dc.date | 2004-07-05 | |
| dc.date | 2006-08-30 | |
| dc.date.accessioned | 2026-07-07T06:38:38Z | |
| dc.date.available | 2026-07-07T06:38:38Z | |
| dc.description | In this article we introduce the mixed Hodge structure of the Brieskorn module of a polynomial $f$ in $\C^{n+1}$, where $f$ satisfies a certain regularity condition at infinity (and hence has isolated singularities). We give an algorithm which produces a basis of a localization of the Brieskorn module which is compatible with its mixed Hodge structure. As an application we show that the notion of a Hodge cycle in regular fibers of $f$ is given in terms of the vanishing of integrals of certain polynomial $n$-forms in $\C^{n+1}$ over topological $n$-cycles on the fibers of $f$. Since the $n$-th homology of a regular fiber is generated by vanishing cycles, this leads us to study Abelian integrals over them. Our result generalizes and uses the arguments of J. Steenbrink 1977 for quasi-homogeneous polynomials. | |
| dc.description | 22 pages, minor corrections, To appear in Ann. Ins. Fourier | |
| dc.identifier | https://arxiv.org/abs/math/0407064 | |
| dc.identifier | http://arxiv.org/abs/math/0407064 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100805 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 14C30, 32S35 | |
| dc.title | Mixed Hodge structure of affine hypersurfaces | |
| dc.type | text |