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arXiv · 2512.06145

Periodic sharpness of Miyaoka's bound for smooth rational curves

Alex Degtyarev·Sławomir Rams
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Abstract

We determine the maximal number of smooth rational degree d curves on a complex K3-surface of degree 2n provided n is sufficiently large as compared to d>1. We obtain precise characterization of configurations of rational degree d curves for which Miyaoka's bound is sharp for nd odd and n sufficiently large as compared to d.

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Alex Degtyarev, Sławomir Rams. 2025-12-05. Periodic sharpness of Miyaoka's bound for smooth rational curves. https://arxiv.org/abs/2512.06145

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