Une précision concernant le théorème de Noether. (A precision concerning the theorem of Noether)
We use the polynomial description of the infinitesimal variation of Hodge structure of hypersurfaces in \({\mathbb{P}}^ n({\mathbb{C}})\) in order to show the following result: Let d be an integer at least five; let \(S_ d\subset {\mathbb{P}}(H^ 0({\mathcal O}_{{\mathbb{P}}^ 3}(d)))\) be the family of smooth surfaces of degree \(d\) such that \(Pic(S_ d)\neq {\mathbb{Z}}\). \(S_ d\) is a countable union of analytic subsets and we have the theorem: Each component of \(S_ d\) is of codimension at least d-3, with equality holding only for the component consisting of surfaces containing a line.
infinitesimal variation of Hodge structure of hypersurfaces
scientific article; zbMATH DE number 3997985
scientific article