Cyclic coverings and Seshadri constants on smooth surfaces

Abstract

We study the Seshadri constants of cyclic coverings of smooth surfaces. The existence of an automorphism on these surfaces can be used to produce Seshadri exceptional curves. We give a bound for multiple Seshadri constants on cyclic coverings of surfaces with Picard number 1. Morevoer, we apply this method to $n$-cyclic coverings of the projective plane. When $2\le n\le 9$, explicit values are obtained. We relate this problem with the Nagata conjecture.

16 pages. Some results have been added. In particular, the main Theorem of math.AG/0512147 ("A note on multiple Seshadri constants on surfaces ") has been extended