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Remarks on special kinds of the relative log minimal model program

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Abstract

We prove \(\mathbb {R}\)-boundary divisor versions of results proved by Birkar (Publ Math Inst Hautes Études Sci 115(1):325–368, 2012) and Hacon–Xu (Invent Math 192(1):161–195, 2013) on special kinds of the relative log minimal model program.

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Acknowledgements

The author would like to express his gratitude to Professor Osamu Fujino for much useful advice, for many useful discussions, and for offering consistently good answers to his questions. He thanks the referees for many useful comments which improved the paper considerably.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan

    Kenta Hashizume

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  1. Kenta Hashizume
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Correspondence to Kenta Hashizume.

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The author was partially supported by JSPS KAKENHI Grant Number JP16J05875 from JSPS.

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Hashizume, K. Remarks on special kinds of the relative log minimal model program. manuscripta math. 160, 285–314 (2019). https://doi.org/10.1007/s00229-018-1088-y

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  • DOI: https://doi.org/10.1007/s00229-018-1088-y

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