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Compact Kähler manifolds with automorphism groups of maximal rank


Author: De-Qi Zhang
Journal: Trans. Amer. Math. Soc. 366 (2014), 3675-3692
MSC (2010): Primary 32H50, 37C85, 32M05, 14J50, 32Q15
DOI: https://doi.org/10.1090/S0002-9947-2014-06227-2
Published electronically: March 5, 2014
MathSciNet review: 3192612
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Abstract: For an automorphism group $ G$ on an $ n$-dimensional ($ n \ge 3$) normal projective variety or a compact Kähler manifold $ X$ so that $ G$ modulo its subgroup $ N(G)$ of null entropy elements is an abelian group of maximal rank $ n-1$, we show that $ N(G)$ is virtually contained in $ \mathrm {Aut}_0(X)$, the $ X$ is a quotient of a complex torus $ T$ and $ G$ is mostly descended from the symmetries on the torus $ T$, provided that both $ X$ and the pair $ (X, G)$ are minimal.


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Additional Information

De-Qi Zhang
Affiliation: Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076
Email: matzdq@nus.edu.sg

DOI: https://doi.org/10.1090/S0002-9947-2014-06227-2
Keywords: Automorphism group, K\"ahler manifold, Tits alternative, topological entropy
Received by editor(s): August 23, 2012
Published electronically: March 5, 2014
Additional Notes: The author was supported by an ARF of NUS
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.