Symplectic involutions of $K3$ surfaces act trivially on $\mathrm{CH}_0$

Claire Voisin

doi:10.4171/dm/383

JournalsdmVol. 17pp. 851–860

Symplectic involutions of $K 3$ surfaces act trivially on $CH_{0}$

Claire Voisin
Institut de Mathématiques de Jussieu Equipe Topologie et Géométrie algébriques Case 247, 4 Place Jussieu, 75005 Paris, France

$Symplectic involutions of $K3$ surfaces act trivially on $\mathrm{CH}_0$ cover$

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Abstract

A symplectic involution on a $K 3$ surface is an involution which preserves the holomorphic 2-form. We prove that such a symplectic involution acts as the identity on the $C H_{0}$ group of the $K 3$ surface, as predicted by Bloch's conjecture.

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Claire Voisin, Symplectic involutions of $K 3$ surfaces act trivially on $CH_{0}$ . Doc. Math. 17 (2012), pp. 851–860

DOI 10.4171/DM/383