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

Ziqi Liu; Shizhuo Zhang

Paper

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

Abstract

We show that the double dual EPW sextic and double EPW sextic associated with a strongly smooth Gushel--Mukai surface can be realized as moduli spaces of semistable objects with respect to a stability condition on the bounded derived category of it. Also, we observe that double dual EPW surface and double EPW surface associated with a special Gushel--Mukai threefold can be realized as moduli spaces of semistable objects on its Kuznetsov component. As an application, we refine a statement of Bayer and Perry about Gushel--Mukai threefolds with equivalent Kuznetsov components for the special ones.