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On two families of Enriques categories over K3 surfaecs (2412.06921v2)
Published 9 Dec 2024 in math.AG
Abstract: This article studies the moduli spaces of semistable objects related to two families of Enriques categories over K3 surfaces, coming from quartic double solids and special Gushel--Mukai threefolds. In particular, classic geometric constructions are recovered in a modular way, such as the double EPW sextic and cube associated with a general Gushel--Mukai surface, and the Beauville's birational involution on the Hilbert scheme of two points on a quartic K3 surface. In addition, we describe the singular loci in some moduli spaces of semistable objects and an explicit birational involutions on an O'Grady's hyperk\"ahler tenfold.