Characterization of varieties of Fano type via singularities of Cox rings

Gongyo, Yoshinori; Okawa, Shinnosuke; Sannai, Akiyoshi; Takagi, Shunsuke

doi:10.1090/S1056-3911-2014-00641-X

Authors: Yoshinori Gongyo, Shinnosuke Okawa, Akiyoshi Sannai and Shunsuke Takagi
Journal: J. Algebraic Geom. 24 (2015), 159-182
DOI: https://doi.org/10.1090/S1056-3911-2014-00641-X
Published electronically: April 30, 2014
MathSciNet review: 3275656
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Abstract | References | Additional Information

Abstract: We show that every Mori dream space of globally $F$-regular type is of Fano type. As an application, we give a characterization of varieties of Fano type in terms of the singularities of their Cox rings.

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Additional Information

Yoshinori Gongyo
Affiliation: Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Email: gongyo@ms.u-tokyo.ac.jp

Shinnosuke Okawa
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
MR Author ID: 953215
Email: okawa@math.sci.osaka-u.ac.jp

Akiyoshi Sannai
Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
Email: sannai@ms.u-tokyo.ac.jp

Shunsuke Takagi
Affiliation: Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Email: stakagi@ms.u-tokyo.ac.jp

Received by editor(s): April 30, 2012
Received by editor(s) in revised form: November 4, 2012
Published electronically: April 30, 2014
Additional Notes: The first and second authors were partially supported by Grant-in-Aid for JSPS Fellows $\#22\cdot$7399 and $\#22\cdot$849, respectively. The fourth author was partially supported by Grant-in-Aid for Young Scientists (B) 23740024 from JSPS
Dedicated: Dedicated to Professor Yujiro Kawamata on the occasion of his sixtieth birthday
Article copyright: © Copyright 2014 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.