Sur l'application des périodes d'une variation de structure de Hodge attachée aux familles d'hypersurfaces à singularités simples.

Philippe Eyssidieux (1) , Damien Mégy (2)

1 IF - Institut Fourier
2 IECL - Institut Élie Cartan de Lorraine

Let $n$ be a positive even integer and $d$ a positive integer . To every complete family $Z$ of n dimensional degree d hypersurfaces in the projective space with isolated A-D-E singularities we construct according to an idea of Carlson-Toledo a Deligne-Mumford stack $\bar Z$ whose moduli space is $Z$ such that the monodromy representation extends. We study the corresponding periods mapping and establish an infinitesimal Torelli theorem along the isosingular strata of lZ$ under transversality assumptions. We apply this result to prove Steiness of the universal covering space of $\bar Z$.

Mots clés: singular hypersurfaces; Infinitesimal Torelli theorem; Polarisable Hodge Modules

Domaines: Géométrie algébrique [math.AG]

Philippe Eyssidieux, Damien Mégy. Sur l'application des périodes d'une variation de structure de Hodge attachée aux familles d'hypersurfaces à singularités simples.. Commentarii Mathematici Helvetici, 2015, 90 (4), pp.731-759. ⟨hal-00823242⟩