Curves with low Harbourne constants on Kummer and Abelian surfaces

Xavier Roulleau

paper

Curves with low Harbourne constants on Kummer and Abelian surfaces

arXiv:1711.06449

Abstract

We construct and study curves with low H-constants on abelian and K3 surfaces. Using the Kummer $(1 6_{6})$ -configurations on Jacobian surfaces and some $(1 6_{10})$ -configurations of curves on $(1, 3)$ -polarized Abelian surfaces, we obtain examples of configurations of curves of genus $> 1$ on a generic Jacobian K3 surface with H-constants $< - 4$ .

Final version, 12 pages