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arXiv · 1907.04182

24 rational curves on K3 surfaces

Sławomir Rams·Matthias Schütt
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Abstract

Given d in IN, we prove that all smooth K3 surfaces (over any field of characteristic p other than 2,3) of degree greater than 84d^2 contain at most 24 rational curves of degree at most d. In the exceptional characteristics, the same bounds hold for non-unirational K3 surfaces, and we develop analogous results in the unirational case. For d at least 3, we also construct K3 surfaces of any degree greater than 4d(d+1) with 24 rational curves of degree exactly d, thus attaining the above bounds.

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Sławomir Rams, Matthias Schütt. 2019-07-09. 24 rational curves on K3 surfaces. https://doi.org/10.1142/s0219199722500080

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