Cyclic coverings and Seshadri constants on smooth surfaces

Details Cyclic coverings and Seshadri constants on smooth surfaces Cyclic coverings and Seshadri constants on smooth surfaces

2005-11-22

arxiv.org/abs/math/0511547v2

Mathematics

Algebraic Geometry

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

Scientific paper

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 $2\leq n\leq 9$, explicit values are obtained. We relate this problem with the Nagata conjecture.

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