## Kodai Mathematical Journal

### On the Chow groups of certain EPW sextics

Robert Laterveer

#### Abstract

This note is about the Hilbert square $X=S^{[2]}$, where $S$ is a general $K3$ surface of degree 10, and the anti-symplectic birational involution $\iota$ of $X$ constructed by O'Grady. The main result is that the action of $\iota$ on certain pieces of the Chow groups of $X$ is as expected by Bloch's conjecture. Since $X$ is birational to a double EPW sextic $X^\prime$, this has consequences for the Chow ring of the EPW sextic $Y\subset\mathbf{P}^5$ associated to $X^\prime$.

#### Article information

Source
Kodai Math. J., Volume 42, Number 1 (2019), 170-201.

Dates
First available in Project Euclid: 19 March 2019

https://projecteuclid.org/euclid.kmj/1552982512

Digital Object Identifier
doi:10.2996/kmj/1552982512

Mathematical Reviews number (MathSciNet)
MR3934619

Zentralblatt MATH identifier
07081619

#### Citation

Laterveer, Robert. On the Chow groups of certain EPW sextics. Kodai Math. J. 42 (2019), no. 1, 170--201. doi:10.2996/kmj/1552982512. https://projecteuclid.org/euclid.kmj/1552982512