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arXiv · 0912.0135

Le thème d'une période évanescente

Daniel Barlet
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Abstract

In this article we study holomorphic deformations of the filtered Gauss-Manin systems associated to a vanishing period integral. For that purpose we introduce a new sub-class of the class of monogenic (a,b)-modules (Brieskorn modules) which was studied in our previous article [B. 09]. We show that these new objects, called ?themes?, have good functorial properties and that there exists a canonical order on the roots of the corresponding Bernstein polynomial. We construct, for given fundamental invariants, a finite dimensional versal holomorphic family and we show that, when all themes with these fundamental invariants are ?stable?, this versal family is in fact universal. We also give a sufficient condition on the roots of the Bernstein polynomial in order that the previous condition is satisfied. We show with an example that a universal family may not exist for some values of the fundamental invariants.

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Daniel Barlet. 2009-12-01. Le thème d'une période évanescente. https://arxiv.org/abs/0912.0135

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