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Singularities of elliptic curves in \(K3\) surfaces and the Beauville–Voisin zero-cycle

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Abstract

Under some hypotheses on the singular type of the one-parameter family of elliptic curves in a primitively polarized \(K3\) surface \(S\) determined by its polarization (which is expected to be true for a very general polarized \(K3\) surface), we give a more geometric proof of the fact that the second Chern class of \(S\) is equal to \(24 \cdot o_S\) in the Chow group of \(0\)-cycles where \(o_S\) is the Beauville–Voisin canonical \(0\)-cycle.

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Acknowledgments

I would like to thank Claire Voisin for her kindness in sharing her ideas and for many helpful discussions and suggestions. I also thank Xi Chen for interesting e-mail correspondence related to this work.

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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. Singularities of elliptic curves in \(K3\) surfaces and the Beauville–Voisin zero-cycle. Boll Unione Mat Ital 7, 227–242 (2014). https://doi.org/10.1007/s40574-014-0013-x

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  • DOI: https://doi.org/10.1007/s40574-014-0013-x

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