Finite-dimensionality and cycles on powers of surfaces

  • Qizheng Yin

    ETH Zürich, Switzerland

Abstract

For a surface , consider the subring of generated by divisor and diagonal classes (with -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 in the sense of Kimura-O'Sullivan. As a consequence, we obtain examples of whose Hilbert schemes satisfy the Beauville-Voisin conjecture.

Cite this article

Qizheng Yin, Finite-dimensionality and cycles on powers of surfaces. Comment. Math. Helv. 90 (2015), no. 2, pp. 503–511

DOI 10.4171/CMH/362