Potentially non-klt locus and its applications

Sung Rak Choi; Jinhyung Park

doi:10.1007/s00208-015-1317-6

Potentially non-klt locus and its applications

Sung Rak Choi, Jinhyung Park

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	141-166
Number of pages	26
Journal	Mathematische Annalen
Volume	366
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-015-1317-6
Publication status	Published - 2016 Oct 1

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

All Science Journal Classification (ASJC) codes

Mathematics(all)

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N2 - 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 - KX-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.

AB - 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 - KX-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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Potentially non-klt locus and its applications

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