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Extensions of Formal Hodge Structures

Nicola Mazzari
Arxiv ID: 0905.1809Last updated: 11/3/2022
We define and study the properties of the category ${\sf FHS}_n$ 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 ${\sf FHS}_n$. This formula generalizes the classical one to the case of proper but non necessarily smooth complex varieties.

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