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Cyclic Branched Coverings of Surfaces with Abelian Quotient Singularities by Bartolo, E. Artal; Cogolludo-Agustín, J. I.; Martín-Morales, Jorge is a scholarly article available to read on EtoBox.

What is Cyclic Branched Coverings of Surfaces with Abelian Quotient Singularities about?

Esnault-Viehweg developed the theory of cyclic branched coverings $\tilde X\to X$ of smooth surfaces providing a very explicit formula for the decomposition of $H^1(\tilde X,\mathbb{C})$ in terms of a resolution of the ramification locus. Later, the first author applies this to the particular case of coverings of $\mathbb{P}^2$ reducing the problem to a combination of global and local conditions on projective curves. In this paper we extend the above results in three directions: first, the theory is extended to surfaces with quotient singularities, second the ramification locus can be partially resolved and need not be reduced, and finally global and local conditions are given to describe the irregularity of cyclic branched coverings of the weighted projective plane. The techniques required for these results are conceptually different and provide simpler proofs for the classical results. For instance, the local contribution comes from certain modules that have the flavor of quasi-adjunction and multiplier ideals on singular surfaces. As an application, a Zariski pair of curves on a singular surface is described. In particular, we prove the existence of two cuspidal curves of degree

Author

Bartolo, E. Artal; Cogolludo-Agustín, J. I.; Martín-Morales, Jorge

Published

2019

Language

EN