Coble duality for Jacobian Kummer fourfolds

2025/05/20 by Agostini, Daniele, Beri, Pietro, Giovenzana, Franco +1 · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.14490

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.

Citations

• On the generalised Kummer fourfold of the Jacobian of a genus two curve
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• On the cone of curves of an abelian variety
• An intersection number for the punctual Hilbert scheme of a surface

Cited by

• On the generalised Kummer fourfold of the Jacobian of a genus two curve

Related

• On the generalised Kummer fourfold of the Jacobian of a genus two curve
• The Coble hypersurfaces
• Göpel Varieties
• Explicit desingularisation of Kummer surfaces in characteristic two via specialisation
• Hodge theory and Lagrangian planes on generalized Kummer fourfolds