Automorphism groups of positive entropy on projective threefolds

Campana, Frederic; Wang, Fei; Zhang, De-Qi

doi:10.1090/S0002-9947-2013-05838-2

Automorphism groups of positive entropy on projective threefolds
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by Frederic Campana, Fei Wang and De-Qi Zhang PDF

Trans. Amer. Math. Soc. 366 (2014), 1621-1638 Request permission

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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