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arXiv · 2505.14490

Coble duality for Jacobian Kummer fourfolds

Daniele Agostini·Pietro Beri·Franco Giovenzana·Ángel David Ríos Ortiz
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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.

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Daniele Agostini, Pietro Beri, Franco Giovenzana, Ángel David Ríos Ortiz. 2025-05-20. Coble duality for Jacobian Kummer fourfolds. https://arxiv.org/abs/2505.14490

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