Curves with low Harbourne constants on Kummer and abelian surfaces

摘要

We construct and study curves with low H-constants on abelian and K3 surfaces. Using the Kummer $$(16_{6})$$ ( 16 6 ) -configurations on Jacobian surfaces and some $$(16_{10})$$ ( 16 10 ) -configurations of curves on (1,?3)-polarized Abelian surfaces, we obtain examples of configurations of curves of genus $$>1$$ > 1 on a generic Jacobian K3 surface with H-constants $$<-~4$$ < - 4 .