The Fujiki class and positive degree maps

Abstract

We show that a map between complex-analytic manifolds, at least one of which is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain relation of "domination" introduced by Gromov is in fact a partial order.

6 pages; significantly restructured first & last sections; corrected statement of Result 3.4 (formerly Result 4.4); added references; to appear in Complex Manifolds