Double EPW cubes from twisted cubics on Gushel-Mukai fourfolds

Soheyla Feyzbakhsh; Hanfei Guo; Zhiyu Liu; Shizhuo Zhang

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arXiv · 2501.12964

Double EPW cubes from twisted cubics on Gushel-Mukai fourfolds

Soheyla Feyzbakhsh·Hanfei Guo·Zhiyu Liu·Shizhuo Zhang

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Abstract

In this paper, we conduct the first systematic investigation of twisted cubics on Gushel-Mukai (GM) fourfolds. We then study the double EPW cube, a 6-dimensional hyperk\"ahler manifold associated with a general GM fourfold $X$, through the Bridgeland moduli space, and show that it is the maximal rationally connected (MRC) quotient of the Hilbert scheme of twisted cubics on $X$. We also prove that a general double EPW cube admits a covering by Lagrangian subvarieties constructed from the Hilbert schemes of twisted cubics on GM threefolds, which provides a new example for a conjecture of O'Grady.

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Soheyla Feyzbakhsh, Hanfei Guo, Zhiyu Liu, Shizhuo Zhang. 2025-01-22. Double EPW cubes from twisted cubics on Gushel-Mukai fourfolds. https://arxiv.org/abs/2501.12964

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