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

• Artal Bartolo, Enrique ^[1] ; Cogolludo Agustín, José Ignacio ^[1] ; Martín Morales, Jorge ^[1]
  1. [1] Universidad de Zaragoza

     Universidad de Zaragoza

     Zaragoza, España

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 68, Nº. 2, 2024, págs. 359-406
• Idioma: inglés
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• Resumen

  • 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.