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arXiv · 1208.0916

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

Claire Voisin
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Abstract

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 canonical 0-cycles $kc_X$ : this is the only 0-cycle on $X$ whose orbit under rational equivalence is of dimension $k$. Using this, we extend results of Huybrechts and O'Grady concerning Chern classes of simple vector bundles on $K3$ surfaces.

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Claire Voisin. 2013-07-10. Rational equivalence of 0-cycles on $K3$ surfaces and conjectures of Huybrechts and O'Grady. https://arxiv.org/abs/1208.0916

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