English

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

Algebraic Geometry 2026-05-26 v4

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.

Keywords

Cite

@article{arxiv.2512.13269,
  title  = {EPW varieties as moduli spaces on ordinary GM surfaces and special GM threefolds},
  author = {Ziqi Liu and Shizhuo Zhang},
  journal= {arXiv preprint arXiv:2512.13269},
  year   = {2026}
}

Comments

30 pages. v4: major revision, remove the Appendix and some claims, add mild assumption for some corollaries