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arXiv · 1602.04063

Combinatorial degenerations of surfaces and Calabi--Yau threefolds

Bruno Chiarellotto·Christopher Lazda
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Abstract

In this article we study combinatorial degenerations of minimal surfaces of Kodaira dimension 0 over local fields, and in particular show that the `type' of the degeneration can be read off from the monodromy operator acting on a suitable cohomology group. This can be viewed as an arithmetic analogue of results of Persson and Kulikov on degenerations of complex surfaces, and extends various particular cases studied by Matsumoto, Liedtke/Matsumoto and Hernández-Mada. We also study `maximally unipotent' degenerations of Calabi--Yau threefolds, following Kollár/Xu, showing in this case that the dual intersection graph is a 3-sphere.

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Bruno Chiarellotto, Christopher Lazda. 2017-01-18. Combinatorial degenerations of surfaces and Calabi--Yau threefolds. https://doi.org/10.2140/ant.2016.10.2235

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