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arXiv · 2512.13269

EPW varieties as moduli spaces on ordinary GM surfaces and special GM threefolds

Ziqi Liu·Shizhuo Zhang
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Abstract

We show that the double dual EPW sextic associated with a strongly smooth Gushel-Mukai surface can be realized as a moduli space of semistable objects on its bounded derived category. Also, we observe that the double dual EPW surface associated with a special Gushel-Mukai threefold can be realized as a moduli space of semistable objects on its Kuznetsov component. Then we discuss extensions of our main results to double EPW sextics and double EPW surfaces and a refinement of a statement of Bayer and Perry about Gushel-Mukai threefolds with equivalent Kuznetsov components, under a mild assumption.

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Ziqi Liu, Shizhuo Zhang. 2025-12-15. EPW varieties as moduli spaces on ordinary GM surfaces and special GM threefolds. https://doi.org/10.1017/nmj.2026.10127

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