arXiv subjects

Calla Tschanz

Publications and source records attributed to Calla Tschanz.

3 recordsLinked to original sources

arXiv2025

From logarithmic Hilbert schemes to degenerations of hyperk\"ahler varieties

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.

math.AG↗

arXiv2024

Good models of Hilbert schemes of points over semistable degenerations

In this paper, we explore different possible choices of expanded degenerations and define appropriate stability conditions in order to construct good degenerations of Hilbert schemes of points over semistable degenerations of surfaces, given as proper Deligne-Mumford stacks. These stacks provide explicit examples of constructions arising from the work of Maulik and Ranganathan. This paper builds upon and generalises previous work in which we constructed a special example of such a stack. We also explain how these methods apply to constructing minimal models of type III degenerations of hyperkähler varieties, namely Hilbert schemes of points on K3 surfaces.

math.AG↗

arXiv2023

Expansions for Hilbert schemes of points on semistable degenerations

The aim of this paper is to extend the expanded degeneration construction of Li and Wu to obtain good degenerations of Hilbert schemes of points on semistable families of surfaces, as well as to discuss alternative stability conditions and parallels to the GIT construction of Gulbrandsen, Halle and Hulek and logarithmic Hilbert scheme constructions of Maulik and Ranganathan. We construct a good degeneration of Hilbert schemes of points as a proper Deligne-Mumford stack and show that it provides a geometrically meaningful example of a construction arising from the work of Maulik and Ranganathan.

math.AG↗