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The Lüroth Problem

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Rationality Problems in Algebraic Geometry

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2172))

Abstract

The Lüroth problem asks whether every unirational variety is rational. After a historical survey, we describe the methods developed in the 1970s to get a negative answer, and give some easy examples. Then we discuss a new method introduced last year by C. Voisin.

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Notes

  1. 1.

    Fano proved in [F3] that the variety X 14 is birational to a smooth cubic threefold.

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Authors and Affiliations

  1. Laboratoire J.-A. Dieudonné, UMR 7351 du CNRS, Université Côte d’Azur, Parc Valrose, F-06108, Nice Cedex 2, France

    Arnaud Beauville

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  1. Arnaud Beauville
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Correspondence to Arnaud Beauville .

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Editors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa Dipartimento di Matematica, Pisa, Italy

    Rita Pardini

  2. Dipartimento di matematica, University of Pavia, Pavia, Italy

    Gian Pietro Pirola

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Beauville, A. (2016). The Lüroth Problem. In: Pardini, R., Pirola, G. (eds) Rationality Problems in Algebraic Geometry. Lecture Notes in Mathematics(), vol 2172. Springer, Cham. https://doi.org/10.1007/978-3-319-46209-7_1

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