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Irrationality issues for projective surfaces

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A Correction to this article was published on 08 January 2018

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Abstract

This survey retraces the author’s talk at the Workshop Birational geometry of surfaces, Rome, January 11–15, 2016. We consider various birational invariants extending the notion of gonality to projective varieties of arbitrary dimension, and measuring the failure of a given projective variety to satisfy certain rationality properties, such as being uniruled, rationally connected, unirational, stably rational or rational. Then we review a series of results describing these invariants for various classes of projective surfaces.

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Change history

  • 08 January 2018

    The purpose of this note is to fix an imprecision in Theorem 3.3 of the original paper, which affects the correctness of the statement and leads to a mistake

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Acknowledgements

I would like to thank the Organizers of the Workshop Birational geometry of surfaces and Andrea Bruno for encouraging me to think about this topic in view of the Workshop. I am grateful to Gian Pietro Pirola for introducing me to these problems when I was a Ph.D. student. I would also like to thank Andreas Knutsen for valuable suggestions.

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Author notes

  1. Francesco Bastianelli

    Present address: Dipartimento di Matematica, Università degli Studi di Bari, Via Edoardo Orabona 4, 70125, Bari, Italy

Authors and Affiliations

  1. Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136, Trieste, Italy

    Francesco Bastianelli

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  1. Francesco Bastianelli
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Correspondence to Francesco Bastianelli.

Additional information

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Grant agreement no. 307119, MIUR FIRB 2012 “Spazi di moduli e applicazioni”, MIUR PRIN 2010–2011“Geometria delle varietà algebriche”, and INdAM (GNSAGA).

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Bastianelli, F. Irrationality issues for projective surfaces. Boll Unione Mat Ital 11, 13–25 (2018). https://doi.org/10.1007/s40574-017-0116-2

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