Cyclic coverings of rational normal surfaces which are quotients of a product of curves

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Enrique Artal Bartolo
Universidad de Zaragoza. Departamento de Matemáticas
https://orcid.org/0000-0002-8276-5116
José Ignacio Cogolludo Agustín
Universidad de Zaragoza. Departamento de Matemáticas
https://orcid.org/0000-0003-1820-6755
Jorge Martín Morales
Universidad de Zaragoza. Departamento de Matemáticas
https://orcid.org/0000-0002-6559-4722

This paper deals with cyclic covers of a large family of rational normal surfaces that can also be described as quotients of a product, where the factors are cyclic covers of algebraic curves. We use a generalization of the Esnault–Viehweg method to show that the action of the monodromy on the first Betti group of the covering (and its Hodge structure) splits as a direct sum of the same data for some specific cyclic covers over P 1. This has applications to the study of Lˆe–Yomdin surface singularities, in particular to the action of the monodromy on the mixed Hodge structure, as well as to isotrivial fibered surfaces.

Paraules clau
Normal surfaces, Cyclic coverings, Alexander polynomial, Monodromy, Isotrivial fibered surfaces, Lê-Yomdin singularities

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Artal Bartolo, Enrique et al. «Cyclic coverings of rational normal surfaces which are quotients of a product of curves». Publicacions Matemàtiques, 2024, vol.VOL 68, núm. 2, p. 359-06, http://raco.cat/index.php/PublicacionsMatematiques/article/view/430114.
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