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Existence of log canonical modifications and its applications

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Abstract

The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some suitable assumptions. Then we recover Kawakita’s inversion of adjunction on log canonicity in full generality. We also discuss the existence of semi-log canonical modifications for demi-normal pairs and construct dlt blow-ups with several extra good properties. As an application, we study lengths of extremal rational curves.

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Acknowledgements

The authors thank Christopher Hacon very much for answering their question. They also thank the referee for many useful comments and suggestions.

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Authors and Affiliations

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

    Osamu Fujino & Kenta Hashizume

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  1. Osamu Fujino
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  2. Kenta Hashizume
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Correspondence to Kenta Hashizume.

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Osamu Fujino was partially supported by JSPS KAKENHI Grant Numbers JP16H03925, JP16H06337. Kenta Hashizume was partially supported by JSPS KAKENHI Grant Numbers JP16J05875, JP19J00046.

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Fujino, O., Hashizume, K. Existence of log canonical modifications and its applications. European Journal of Mathematics 9, 13 (2023). https://doi.org/10.1007/s40879-023-00598-0

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  • DOI: https://doi.org/10.1007/s40879-023-00598-0

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