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New outlook on the Minimal Model Program, II

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Abstract

We prove that the finite generation of adjoint rings implies all the foundational results of the Minimal Model Program: the Rationality, Cone and Contraction theorems, the existence of flips, and termination of flips with scaling in the presence of a big boundary.

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Notes

  1. This was done first in [14], surveyed in [3]. The paper [2] is an evolution and replacement of [14] using several of the original ideas and constructions.

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Acknowledgments

We would like to thank P. Cascini, F. Catanese, S. Coughlan, O. Fujino, A.-S. Kaloghiros, K. Matsuki and M. Mustaţă for many useful conversations and comments. We are grateful to the referee for many useful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, UK

    Alessio Corti

  2. Mathematisches Institut, Universität Bayreuth, 95440 , Bayreuth, Germany

    Vladimir Lazić

Authors
  1. Alessio Corti
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  2. Vladimir Lazić
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Correspondence to Vladimir Lazić.

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Corti, A., Lazić, V. New outlook on the Minimal Model Program, II. Math. Ann. 356, 617–633 (2013). https://doi.org/10.1007/s00208-012-0858-1

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  • DOI: https://doi.org/10.1007/s00208-012-0858-1

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