Coble duality for Jacobian Kummer fourfolds
Algebraic Geometry
2025-05-28 v2
Abstract
We study projective models of generalized Kummer fourfolds via O'Grady's theta groups and the classical Coble cubic. More precisely, we establish a duality between two singular models of the generalized Kummer fourfold of a Jacobian abelian surface. We also give projective models for singular Jacobian Kummer varieties of arbitrary dimension. Along the way, we also construct a first non-natural involution on the Hilbert square of a Jacobian surface. In the appendix, we study singularities of secants of arbitrary varieties at identifiable points, following Choi, Lacini, Park and Sheridan.
Cite
@article{arxiv.2505.14490,
title = {Coble duality for Jacobian Kummer fourfolds},
author = {Daniele Agostini and Pietro Beri and Franco Giovenzana and Ángel David Ríos Ortiz},
journal= {arXiv preprint arXiv:2505.14490},
year = {2025}
}
Comments
42 pages. Typos fixed, bibliography updated