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arXiv · 2601.21871

Polync varieties and multiparameter Kulikov models

Philip Engel
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Abstract

We study "polync varieties", whose singularities are locally products of normal crossing (nc) singularities. We introduce the notion of d-semistability of such varieties, and generalize work of Friedman and Kawamata-Namikawa to address the smoothability of d-semistable, K-trivial, polync varieties. These results are applications of recent breakthroughs on the logarithmic Bogomolov-Tian-Todorov theorem, due to Chan-Leung-Ma and Felten-Filip-Ruddat. We generalize the combinatorial description of Kulikov models for K3 surfaces to the setting of a multiparameter base and describe some interesting examples.

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Philip Engel. 2026-01-29. Polync varieties and multiparameter Kulikov models. https://arxiv.org/abs/2601.21871

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