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arXiv · 2507.15695

Combinatorics and Hodge theory of degenerations of abelian varieties: A survey of the Mumford construction

Philip Engel·Olivier de Gaay Fortman·Stefan Schreieder
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Abstract

We survey the Mumford construction of degenerating abelian varieties, with a focus on the analytic version of the construction, and its relation to toric geometry. Moreover, we study the geometry and Hodge theory of multivariable degenerations of abelian varieties associated to regular matroids, and extend some fundamental results of Clemens on 1-parameter semistable degenerations to the multivariable setting.

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Philip Engel, Olivier de Gaay Fortman, Stefan Schreieder. 2025-07-21. Combinatorics and Hodge theory of degenerations of abelian varieties: A survey of the Mumford construction. https://arxiv.org/abs/2507.15695

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