JournalsjemsVol. 12 , No. 6DOI 10.4171/jems/240

Chow groups of K3 surfaces and spherical objects

  • Daniel Huybrechts

    Universität Bonn, Germany
Chow groups of K3 surfaces and spherical objects cover

Abstract

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 [5], Lazarfeld’s result on Brill–Noether theory for curves in K3 surfaces [15] and the deformation theory developed in [12] are central for the discussion.