论文标题
零循环在双EPW六元上
Zero-cycles on double EPW sextics
论文作者
论文摘要
Hyperkähler品种的盘子环具有特别丰富的结构。在本文中，我们专注于本地完整的双重EPW六六元家族，并建立了其Chow环的一些属性。首先，我们证明了Beauville-voisin型定理，用于双EPW六六元的零循环；确切地说，我们表明，由除数产生的双EPW六六元的Cyimension-4部分，Chern类和Codimension-2循环在反连续性覆盖范围下不变的conern类和Codimension-2循环排名第一。其次，对于K3表面的Hilbert Square的双重EPW六序列化，我们表明抗隔离式相互作用对零循环的Chow群的作用与Shen-Vial的傅立叶分解。
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.
