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Birational Invariants and Decomposition of the Diagonal

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Birational Geometry of Hypersurfaces

Part of the book series: Lecture Notes of the Unione Matematica Italiana ((UMILN,volume 26))

Abstract

We give a rather detailed account of cohomological and Chow-theoretic methods in the study of the stable version of the Lroth problem, which ask how to distinguish (stably) rational varieties from general unirational varieties. In particular, we study the notion of Chow or cohomological decomposition of the diagonal, which is a necessary criterion for stable rationality. Having better stability properties than the previously known obstructions under specialization with mildly singular central fibers, it has been very useful in the recent study of rationality questions.

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Authors and Affiliations

  1. Collège de France, Paris, France

    Claire Voisin

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  1. Claire Voisin
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Correspondence to Claire Voisin .

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Editors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Andreas Hochenegger

  2. Institut für Mathematik, Johannes Gutenberg Universität Mainz, Mainz, Germany

    Manfred Lehn

  3. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Paolo Stellari

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Voisin, C. (2019). Birational Invariants and Decomposition of the Diagonal. In: Hochenegger, A., Lehn, M., Stellari, P. (eds) Birational Geometry of Hypersurfaces. Lecture Notes of the Unione Matematica Italiana, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-030-18638-8_1

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