The dimension of automorphism groups of algebraic varieties with pseudo-effective log canonical divisors
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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