Polync varieties and multiparameter Kulikov models

2026/01/31 by Philip Engel
Mathematics · #math.AG #math.SG

paper · pdf

22 pages, 7 figures. v2: some corrections and added material

arxiv created 2026/08/01 · arxiv updated 2026/08/04

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.

Citations

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