Finite-dimensionality and cycles on powers of K3 surfaces
Algebraic Geometry
2014-10-20 v2
Abstract
For a K3 surface S, consider the subring of CH(S^n) generated by divisor and diagonal classes (with Q-coefficients). Voisin conjectures that the restriction of the cycle class map to this ring is injective. We prove that Voisin's conjecture is equivalent to the finite-dimensionality of S in the sense of Kimura-O'Sullivan. As a consequence, we obtain examples of S whose Hilbert schemes satisfy the Beauville-Voisin conjecture.
Keywords
Cite
@article{arxiv.1404.0171,
title = {Finite-dimensionality and cycles on powers of K3 surfaces},
author = {Qizheng Yin},
journal= {arXiv preprint arXiv:1404.0171},
year = {2014}
}
Comments
7 pages. Section 2.6 rewritten, typos fixed and further references added