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On Quasi-Étale Quotients of a Product of Two Curves

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Beauville Surfaces and Groups

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 123))

Abstract

A quasi-étale quotient of a product of two curves is the quotient of a product of two curves by the action of a finite group which acts freely out of a finite set of points. A quasi-étale surface is the minimal resolution of the singularities of a quasi-étale quotient. They have been successfully used in the last years by several authors to produce several interesting new examples of surfaces. In this paper we describe the principal results on this class of surfaces, and report the full list of the minimal quasi-étale surfaces of general type with geometric genus equal to the irregularity \({\le }2\).

The author was partially supported by the projects PRIN2010-2011 Geometria delle varietà algebriche and Futuro in Ricerca 2012 Moduli Spaces and Applications.

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Authors and Affiliations

  1. Dipartimento di Matematica dell’Università di Trento, Via Sommarive 14, 38123, Trento, TN, Italy

    Roberto Pignatelli

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  1. Roberto Pignatelli
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Correspondence to Roberto Pignatelli .

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Editors and Affiliations

  1. Lehrstuhl Mathematik VIII, University of Bayreuth, Bayreuth, Germany

    Ingrid Bauer

  2. Institut für Mathematische Logik und Gru, University of Münster, Münster, Germany

    Shelly Garion

  3. School of Mathematics and Statistics, Newcastle University, Newcastle-upon-Tyne, United Kingdom

    Alina Vdovina

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Pignatelli, R. (2015). On Quasi-Étale Quotients of a Product of Two Curves. In: Bauer, I., Garion, S., Vdovina, A. (eds) Beauville Surfaces and Groups. Springer Proceedings in Mathematics & Statistics, vol 123. Springer, Cham. https://doi.org/10.1007/978-3-319-13862-6_10

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