Extensions of Formal Hodge Structures

Abstract

We define and study the properties of the category ${\mathsf{FHS}}_n$ of formal Hodge structure of level $\le n$ following the ideas of L. Barbieri-Viale who discussed the case of level $\le 1$. As an application we describe the generalized Albanese variety of Esnault, Srinivas and Viehweg via the group $\Ext^1$ in ${\mathsf{FHS}}_n$. This formula generalizes the classical one to the case of proper but non necessarily smooth complex varieties.

23 pages