Chow groups of K3 surfaces and spherical objects
Daniel HuybrechtsUniversität Bonn, Germany
We show that for a K3 surface X the finitely generated subring R (X) ⊂ CH* (X) introduced by Beauville and Voisin is preserved under derived equivalences. This is proved by analyzing Chern characters of spherical bundles (and complexes). As for a K3 surface X defined over a number field all spherical bundles on the complex K3 surface _X_ℂ are defined over ℚ, this is compatible with the Bloch–Beilinson conjecture. Besides the work of Beauville and Voisin , Lazarfeld’s result on Brill–Noether theory for curves in K3 surfaces  and the deformation theory developed in  are central for the discussion.
Cite this article
Daniel Huybrechts, Chow groups of K3 surfaces and spherical objects. J. Eur. Math. Soc. 12 (2010), no. 6, pp. 1533–1551DOI 10.4171/JEMS/240