Geodesic
Chow groups of K3 surfaces and spherical objects
Journal of the European Mathematical Society, Tome 12 (2010) no. 6, pp. 1533-1551.

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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 XC​ are defined over Qˉ​, 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.
DOI : 10.4171/jems/240
Classification : 14-XX, 00-XX 
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     author = {Daniel Huybrechts},
     title = {Chow groups of {K3} surfaces and spherical objects},
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Daniel Huybrechts. Chow groups of K3 surfaces and spherical objects. Journal of the European Mathematical Society, Tome 12 (2010) no. 6, pp. 1533-1551. doi : 10.4171/jems/240. http://geodesic.mathdoc.fr/articles/10.4171/jems/240/

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