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Cohomological and Geometric Approaches to Rationality Problems pp 275–311Cite as

The Rationality Problem and Birational Rigidity

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Part of the book series: Progress in Mathematics ((PM,volume 282))

Summary

In this survey paper birational geometry of higher-dimensional rationally connected varieties is discussed. In higher dimensions the classical rationality problem generalizes to the problem of description of the structures of a rationally connected fiber space on a given variety. We discuss the key concept of birational rigidity and present examples of Fano fiber spaces with finitely many rationally connected structures.

2000 Mathematics Subject Classification codes: 14E08, 14E05

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Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Liverpool Liverpool, Peach Street, M& O Building, L69 7ZL, Liverpool, UK

    Aleksandr V. Pukhlikov

Authors
  1. Aleksandr V. Pukhlikov
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Correspondence to Aleksandr V. Pukhlikov .

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Editors and Affiliations

  1. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, USA

    Fedor Bogomolov

  2. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Yuri Tschinkel

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Pukhlikov, A.V. (2010). The Rationality Problem and Birational Rigidity. In: Bogomolov, F., Tschinkel, Y. (eds) Cohomological and Geometric Approaches to Rationality Problems. Progress in Mathematics, vol 282. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4934-0_11

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