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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The dimension of automorphism groups of algebraic varieties with pseudo-effective log canonical divisors
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by Fei Hu PDF
Proc. Amer. Math. Soc. 146 (2018), 1879-1893 Request permission

Abstract:

Let $(X,D)$ be a log smooth pair of dimension $n$, where $D$ is a reduced effective divisor such that the log canonical divisor $K_X + D$ is pseudo-effective. Let $G$ be a connected algebraic subgroup of $\rm {Aut}(X, D)$. We show that $G$ is a semi-abelian variety of dimension $\le \min \{n-\bar {\kappa }(V), n\}$ with $V\coloneq X\setminus D$. In the dimension two, Iitaka claimed in his 1979 Osaka J. Math. paper that $\dim G\le \bar {q}(V)$ for a log smooth surface pair with $\bar {\kappa }(V) = 0$ and $\bar {p}_g(V) = 1$. We (re-)prove and generalize this classical result for all surfaces with $\bar {\kappa }=0$ without assuming Iitaka’s classification of logarithmic Iitaka surfaces or logarithmic $K3$ surfaces.
References
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Additional Information
  • Fei Hu
  • Affiliation: Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076
  • Address at time of publication: Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2
  • MR Author ID: 1086386
  • Email: hf@u.nus.edu
  • Received by editor(s): February 16, 2017
  • Received by editor(s) in revised form: June 28, 2017, and June 30, 2017
  • Published electronically: December 4, 2017
  • Communicated by: Lev Borisov
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 1879-1893
  • MSC (2010): Primary 14J50, 14L10, 14L30
  • DOI: https://doi.org/10.1090/proc/13893
  • MathSciNet review: 3767343