Smoothing cones over K3 surfaces

Coughlan, Stephen; Sano, Taro

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Journal Article

Smoothing cones over K3 surfaces

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Sano, Taro
Max Planck Institute for Mathematics, Max Planck Society;

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https://hal.archives-ouvertes.fr/hal-01627067v2
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arXiv:1601.02381.pdf
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Coughlan-Sano_Smoothing cones over K5 surfaces_2018.pdf
(Publisher version), 565KB

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Citation

Coughlan, S., & Sano, T. (2018). Smoothing cones over K3 surfaces. Épijournal de Géométrie Algébrique, 2: 15. Retrieved from http://arxiv.org/abs/1601.02381.

Cite as: https://hdl.handle.net/21.11116/0000-0004-47C9-A

Abstract

We prove that the affine cone over a general primitively polarised K3 surface of genus g is smoothable if and only if g\le 10 or g=12. We also give several examples of singularities with special behaviour, such as surfaces whose affine cone is smoothable even though the projective cone is not.