Conics on Gushel–Mukai fourfolds, EPW sextics and Bridgeland moduli spaces

Abstract

We identify the double dual EPW sextic ỸA⊥ and the double EPW sextic ỸA, associated with a very general Gushel–Mukai fourfold X, with the Bridgeland moduli spaces of stable objects of character Λ1 and Λ2 in the Kuznetsov component Ku(X). This provides an affirmative answer to a question of Perry–Pertusi–Zhao. As an application, we prove a conjecture of Kuznetsov–Perry for very general Gushel–Mukai fourfolds. © 2024 International Press, Inc.. All rights reserved.