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About Chow groups of certain hyperk\"ahler varieties with non-symplectic automorphisms by Laterveer, Robert is a scholarly article available to read on EtoBox.

What is About Chow groups of certain hyperk\"ahler varieties with non-symplectic automorphisms about?

Let $X$ be a hyperk\"ahler variety, and let $G$ be a group of finite order non-symplectic automorphisms of $X$. Beauville's conjectural splitting property predicts that each Chow group of $X$ should split in a finite number of pieces. The Bloch-Beilinson conjectures predict how $G$ should act on these pieces of the Chow groups: certain pieces should be invariant under $G$, while certain other pieces should not contain any non-trivial $G$-invariant cycle. We can prove this for two pieces of the Chow groups when $X$ is the Hilbert scheme of a $K3$ surface and $G$ consists of natural automorphisms. This has consequences for the Chow ring of the quotient $X/G$.

Author

Laterveer, Robert

Published

2017

Language

EN