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Potentially non-klt locus and its applications

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Abstract

We introduce the notion of potentially klt pairs for normal projective varieties with pseudoeffective anticanonical divisor. The potentially non-klt locus is a subset of X which is birationally transformed precisely into the non-klt locus on a \(-K_X\)-minimal model of X. We prove basic properties of potentially non-klt locus in comparison with those of classical non-klt locus. As applications, we give a new characterization of varieties of Fano type, and we also improve results on the rational connectedness of uniruled varieties with pseudoeffective anticanonical divisor.

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Acknowledgments

We would like to thank professors Vyacheslav V. Shokurov for valuable suggestions, Florin Ambro for interesting discussions, and Yoshinori Gongyo for useful comments. S. Choi was supported by supported by IBS-R003-D1.

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Authors and Affiliations

  1. Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, 37673, Republic of Korea

    Sung Rak Choi

  2. School of Mathematics, Korea Institute for Advanced Study (KIAS), Seoul, 02455, Republic of Korea

    Jinhyung Park

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  1. Sung Rak Choi
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  2. Jinhyung Park
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Correspondence to Jinhyung Park.

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Choi, S.R., Park, J. Potentially non-klt locus and its applications. Math. Ann. 366, 141–166 (2016). https://doi.org/10.1007/s00208-015-1317-6

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  • DOI: https://doi.org/10.1007/s00208-015-1317-6

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