Polync varieties and multiparameter Kulikov models
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911407055831040 |
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| author | Engel, Philip |
| author_facet | Engel, Philip |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21871 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Polync varieties and multiparameter Kulikov models Engel, Philip Algebraic Geometry Symplectic Geometry 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. |
| title | Polync varieties and multiparameter Kulikov models |
| topic | Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2601.21871 |