From logarithmic Hilbert schemes to degenerations of hyperk\"ahler varieties
Algebraic Geometry
2025-12-25 v1
Abstract
We construct the first examples of good type III degenerations of hyperk\"ahler varieties in dimension greater than 2. These are presented as moduli of 0-dimensional subschemes on expansions of a degeneration of K3 surfaces. We prove projectivity for our expanded degenerations and compute the dual complexes of the special fibre for two specific degenerations of hyperkahler fourfolds. Moreover, we explain the correspondence between geometric strata of the special fibre and simplices in its dual complex.
Keywords
Cite
@article{arxiv.2512.21190,
title = {From logarithmic Hilbert schemes to degenerations of hyperk\"ahler varieties},
author = {Qaasim Shafi and Calla Tschanz},
journal= {arXiv preprint arXiv:2512.21190},
year = {2025}
}
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21 pages