Sections hyperplanes \`a singularit\'es simples et exemples de variations de structure de Hodge

TL;DR

This paper constructs complex projective varieties with variations of Hodge structure in dimensions 3 to 6, generalizing previous 2D examples, and investigates their properties, especially cohomology groups.

Contribution

It introduces new higher-dimensional examples of varieties with variations of Hodge structure, extending prior 2D constructions and analyzing their cohomological properties.

Findings

Construction of smooth projective varieties in dimensions 3-6 with specified Hodge variations

Analysis of cohomology groups of these varieties

Extension of known 2D examples to higher dimensions

Abstract

We construct smooth complex projective varieties of dimension 3 to 6 with variations of Hodge structure, by generalizing an example of J. Carlson and C. Simpson in dimension 2. Then, we study some of their properties, in particular their cohomology groups.