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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Compact Kähler manifolds with automorphism groups of maximal rank
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by De-Qi Zhang PDF
Trans. Amer. Math. Soc. 366 (2014), 3675-3692 Request permission

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
  • MR Author ID: 187025
  • ORCID: 0000-0003-0139-645X
  • Email: matzdq@nus.edu.sg
  • Received by editor(s): August 23, 2012
  • Published electronically: March 5, 2014
  • Additional Notes: The author was supported by an ARF of NUS
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 3192612