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Isotrivially Fibred Surfaces and Their Numerical Invariants

  • Francesco PolizziEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (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.

Keywords

Isotrivial fibrations Numerical invariants 

2010 Mathematics Subject Classification

14J99 14J29 

Notes

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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità della CalabriaArcavacata RendeItaly

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