Rational equivalence of 0-cycles on $K3$ surfaces and conjectures of Huybrechts and O'Grady

摘要

We give a new interpretation of O'Grady's filtration on the $CH_0$ group of a$K3$ surface. In particular, we get a new characterization of the canonical0-cycles $kc_X$ : this is the only 0-cycle on $X$ whose orbit under rationalequivalence is of dimension $k$. Using this, we extend results of Huybrechtsand O'Grady concerning Chern classes of simple vector bundles on $K3$ surfaces.