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Rational maps from punctual Hilbert schemes of K3 surfaces

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Abstract

The purpose of this article is to study dominant rational maps from punctual Hilbert schemes of length k ≥ 2 of projective K3 surfaces. Precisely, we prove that their image is necessarily rationally connected if the rational map is not generically finite. As an application, we simplify C. Voisin’s proof of the fact that symplectic involutions of any projective K3 surface S act trivially on CH0(S).

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  1. Centre de Mathématiques Laurent Schwartz, 91128, Palaiseau Cédex, France

    Hsueh-Yung Lin

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  1. Hsueh-Yung Lin
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Lin, HY. Rational maps from punctual Hilbert schemes of K3 surfaces. manuscripta math. 146, 531–538 (2015). https://doi.org/10.1007/s00229-014-0710-x

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  • DOI: https://doi.org/10.1007/s00229-014-0710-x

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