GIT stable cubic threefolds and certain fourfolds of $K3^{[2]}$-type
Year: 2025
Type: article
Abstract: We study the behaviour on some nodal hyperplanes of the isomorphism, described by Boissière–Camere–Sarti, between the moduli space of smooth cubic threefolds and the moduli space of hyperkähler fourfolds of K3^{[2]} -type with a non-symplectic automorphism of order three, whose invariant lattice has rank one and is generated by a class of square 6; along those hyperplanes, the automorphism degenerates by jumping to another family. We generalize their result to singular nodal cubic threefolds having one singularity of type A_{i} , for i=2, 3, 4 , providing birational maps between the loci of cubic threefolds where a generic element has an isolated singularity of the types A_{i} and some moduli spaces of hyperkähler fourfolds of K3^{[2]} -type with non-symplectic automorphism of order three belonging to different families. In order to treat the A_{2} case, we introduce the notion of Kähler cone sections of K -type, generalizing the definition of K -general polarized hyperkähler manifolds.
DOI: 10.4171/rmi/1553
Author: Lucas Li Bassi
Institution: University of Genoa
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409412501