Abstract: Similarly to the case of a cubic fourfold, a Gushel-Mukai fourfold has an associated K3 category and an irreducible holomorphic symplectic variety (the dual double EPW sextic). In this talk, we will discuss the relation between the group of 1-cycles on a Gushel-Mukai fourfold and the group of 0-cycles on the corresponding dual double EPW sextic. We proved that the invariant locus of a general dual double EPW sextic is a constant cycle surface. We also use the Beauville-Voisin filtration on a dual double EPW sextic to define a filtration on the group of 1-cycles on the Gushel-Mukai fourfold and conjecture a sheaf/cycle correspondence for the associated K3 category.

#Tencent/Voov meeting：180-914-163
Passcode：544992