2013/04/15 by Truong, Tuyen Trung
#32H50 #37F99 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1304.4100
Let X be a compact Kähler manifold of dimension 3 and let f:X→ X be a pseudo-automorphism. Under the mild condition that λ1(f)2>λ2(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 equidistribution result (which is essentially known in the literature) for Green (1,1) currents of meromorphic selfmaps, not necessarily 1-algebraic 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 are well-defined with respect to our definition here, even though not obviously to be seen so using the usual criteria.