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Transactions of the American Mathematical Society

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

   
 
 

 

Some dynamical properties of pseudo-automorphisms in dimension $3$


Author: Tuyen Trung Truong
Journal: Trans. Amer. Math. Soc. 368 (2016), 727-753
MSC (2010): Primary 37F99, 32H50
DOI: https://doi.org/10.1090/S0002-9947-2014-06340-X
Published electronically: December 16, 2014
MathSciNet review: 3413882
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Abstract: Let $X$ be a compact Kähler manifold of dimension $3$ and let $f:X\rightarrow X$ be a pseudo-automorphism. Under the mild condition that $\lambda _1(f)^2>\lambda _2(f)$, we prove the existence of invariant positive closed $(1,1)$ and $(2,2)$ currents, and we also discuss the (still open) problem of intersection of such currents. We prove a weak equi-distribution result for Green $(1,1)$ currents of meromorphic selfmaps, not necessarily algebraic $1$-stable, of a compact Kähler manifold of arbitrary dimension and discuss how a stronger equidistribution result may be proved for pseudo-automorphisms in dimension $3$. As a byproduct, we show that the intersection of some dynamically related currents is well-defined with respect to our definition here, even though not obviously to be seen so using the usual criteria.


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Additional Information

Tuyen Trung Truong
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
Address at time of publication: School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea
MR Author ID: 724811
Email: tutruong@syr.edu, truong@kias.re.kr

Keywords: Dynamical degrees, intersection of currents, invariant currents, pseudo-automorphisms, pullback of currents, quasi-potentials.
Received by editor(s): May 8, 2013
Received by editor(s) in revised form: December 3, 2013
Published electronically: December 16, 2014
Article copyright: © Copyright 2014 by the author