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Uniruledness of stable base loci of adjoint linear systems via Mori theory

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Abstract

We explain how to deduce from recent results in the Minimal Model Program a general uniruledness theorem for base loci of adjoint divisors. As a special case, we recover previous results by Takayama.

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Notes

  1. After the posting of this article on the arXiv, Cacciola and Di Biagio [4] proved the conjecture for surfaces and, in dimension \(\ge \)3, in the klt case.

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Acknowledgments

We would like to thank Stéphane Druel for interesting exchanges related to this work. Part of this work was done by G.P. during his stay at the Università di Roma “La Sapienza”, and he wishes to thank Kieran O’Grady for making this stay very pleasant and stimulating and for providing the financial support. A.B. thanks Laurent Bonavero for stimulating conversations on this subject. Finally, we are very grateful to the referees for their many useful suggestions.

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Authors and Affiliations

  1. CNRS-Université Pierre et Marie Curie, Institut de Mathématiques, 75251 , Paris Cedex, France

    Sébastien Boucksom

  2. Université Lille 1, UMR CNRS 8524, UFR de mathématiques, 59 655 , Villeneuve d’Ascq Cedex, France

    Amaël Broustet

  3. Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS, 7, Rue R. Descartes, 67084 , Strasbourg Cedex, France

    Gianluca Pacienza

Authors
  1. Sébastien Boucksom
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  2. Amaël Broustet
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  3. Gianluca Pacienza
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Correspondence to Gianluca Pacienza.

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Boucksom, S., Broustet, A. & Pacienza, G. Uniruledness of stable base loci of adjoint linear systems via Mori theory. Math. Z. 275, 499–507 (2013). https://doi.org/10.1007/s00209-013-1144-y

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  • DOI: https://doi.org/10.1007/s00209-013-1144-y

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