2020/04/15 by Robert Laterveer, Laterveer, Robert, Charles Vial +1
Mathematics · #14C15 #14C25 #14J28 #14J42 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C15 #msc:14C25 #msc:14J28 #msc:14J42
paper · pdf · doi:10.48550/arxiv.2004.07005
19 pages. To appear in Commun. Contemp. Math
arxiv created 2020/04/15 · arxiv updated 2020/04/16
The Chow rings of hyperKähler varieties are conjectured to have a particularly rich structure. In this paper, we focus on the locally complete family of double EPW sextics and establish some properties of their Chow rings. First we prove a Beauville-Voisin type theorem for zero-cycles on double EPW sextics; precisely, we show that the codimension-4 part of the subring of the Chow ring of a double EPW sextic generated by divisors, the Chern classes and codimension-2 cycles invariant under the anti-symplectic covering involution has rank one. Second, for double EPW sextics birational to the Hilbert square of a K3 surface, we show that the action of the anti-symplectic involution on the Chow group of zero-cycles commutes with the Fourier decomposition of Shen-Vial.