Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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


Author: Fei Hu
Journal: Proc. Amer. Math. Soc. 146 (2018), 1879-1893
MSC (2010): Primary 14J50, 14L10, 14L30
DOI: https://doi.org/10.1090/proc/13893
Published electronically: December 4, 2017
MathSciNet review: 3767343
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14J50, 14L10, 14L30

Retrieve articles in all journals with MSC (2010): 14J50, 14L10, 14L30


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

Keywords: Automorphism, semi-abelian variety, group action, logarithmic Kodaira dimension
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
Article copyright: © Copyright 2017 American Mathematical Society