Periodic sharpness of Miyaoka's bound for smooth rational curves
arXiv:2512.06145
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.
21 pages