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Cyclic coverings and Seshadri constants on smooth surfaces

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

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Luis Fuentes Garcia. 2006-04-27. Cyclic coverings and Seshadri constants on smooth surfaces. https://arxiv.org/abs/math/0511547

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