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Isotrivially Fibred Surfaces and Their Numerical Invariants

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Beauville Surfaces and Groups

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

Abstract

We give a survey of our previous work on relatively minimal isotrivial fibrations \(\alpha :X \longrightarrow C\), where \(X\) is a smooth, projective surface and \(C\) is a curve. In particular, we consider two inequalities involving the numerical invariants \(K_X^2\) and \(\chi (\mathcal {O}_X)\) and we illustrate them by means of several examples and counter examples.

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Acknowledgments

This paper is an expanded version of the talk given by the author at the conference Beauville surfaces and Groups, Newcastle University (UK), 7–9th June 2012. The author is grateful to the organizers N. Barker, I. Bauer, S. Garion and A. Vdovina for the invitation and the kind hospitality. He was partially supported by Progetto MIUR di Rilevante Interesse Nazionale Geometria delle Variet \(\grave{a}\) Algebriche e loro Spazi di Moduli. He also thanks the referee, whose comments helped to improve the presentation of these results.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università della Calabria, Cubo 30B, 87036, Arcavacata Rende, Cosenza, Italy

    Francesco Polizzi

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  1. Francesco Polizzi
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Correspondence to Francesco Polizzi .

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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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Polizzi, F. (2015). Isotrivially Fibred Surfaces and Their Numerical Invariants. 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_11

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