Periodic sharpness of Miyaoka's bound for smooth rational curves
Algebraic Geometry
2025-12-09 v1
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.
Cite
@article{arxiv.2512.06145,
title = {Periodic sharpness of Miyaoka's bound for smooth rational curves},
author = {Alex Degtyarev and Sławomir Rams},
journal= {arXiv preprint arXiv:2512.06145},
year = {2025}
}
Comments
21 pages