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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Automorphism groups of positive entropy on projective threefolds


Authors: Frederic Campana, Fei Wang and De-Qi Zhang
Journal: Trans. Amer. Math. Soc. 366 (2014), 1621-1638
MSC (2010): Primary 32H50, 14J50, 32M05, 37B40
Published electronically: November 14, 2013
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Abstract: We prove two results about the natural representation of a group $ G$ of automorphisms of a normal projective threefold $ X$ on its second cohomology. We show that if $ X$ is minimal, then $ G$, modulo a normal subgroup of null entropy, is embedded as a Zariski-dense subset in a semi-simple real linear algebraic group of real rank $ \le 2$. Next, we show that $ X$ is a complex torus if the image of $ G$ is an almost abelian group of positive rank and the kernel is infinite, unless $ X$ is equivariantly non-trivially fibred.


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Additional Information

Frederic Campana
Affiliation: Department of Mathematics, University of Nancy 1, BP 239, F-54506, Vandoeuvre-les-Nancy, Cedex, France
Email: Frederic.Campana@iecn.u-nancy.fr

Fei Wang
Affiliation: Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076
Email: matwf@nus.edu.sg

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

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05838-2
PII: S 0002-9947(2013)05838-2
Keywords: Automorphism, iteration, complex dynamics, topological entropy
Received by editor(s): July 12, 2011
Received by editor(s) in revised form: July 25, 2011, September 14, 2011, November 15, 2011, January 9, 2012, March 19, 2012, and March 26, 2012
Published electronically: November 14, 2013
Article copyright: © Copyright 2013 American Mathematical Society