G\"opel Varieties
Algebraic Geometry
2025-07-21 v2
Abstract
We show that the Coble hypersurfaces, uniquely characterized by the remarkable property that their singular loci are an abelian surface and a Kummer threefold, respectively, belong to a family of hypersurfaces exhibiting similar behavior, but defined in various types of homogeneous spaces. With the help of Jordan-Vinberg theory, we show how these hypersurfaces can be parametrized by G{\"o}pel type varieties inside projectivized representations of complex reflection groups.
Cite
@article{arxiv.2506.22030,
title = {G\"opel Varieties},
author = {Vladimiro Benedetti and Michele Bolognesi and Daniele Faenzi and Laurent Manivel},
journal= {arXiv preprint arXiv:2506.22030},
year = {2025}
}
Comments
Ancillary code files (hopefully) added. 48 pages, comments welcome!