The Kuga-Satake construction under degeneration

TL;DR

This paper extends the Kuga-Satake construction to degenerating K3 surfaces, enabling analysis of the associated abelian varieties' geometry and Hodge structures during degeneration.

Contribution

It generalizes the Kuga-Satake construction to limit mixed Hodge structures, providing new tools for studying degenerations of K3 type Hodge structures.

Findings

Extended Kuga-Satake construction to limit mixed Hodge structures

Analyzed degenerations of Kuga-Satake abelian varieties

Enhanced understanding of Hodge theory in degenerations

Abstract

We extend the Kuga-Satake construction to the case of limit mixed Hodge structures of K3 type. We use this to study the geometry and Hodge theory of degenerations of Kuga-Satake abelian varieties, associated to polarized variations of K3 type Hodge structures over the punctured disc.