Compact varieties of surjective holomorphic mappings (Q1088036)

Let X,Y be compact complex varieties. An Aut-orbit in Hol(X,Y) is a subvariety of the form \(g\cdot Aut_ 0(Y')\circ f\) with \(f: X\to Y'\), g: Y'\(\to Y\) holomorphic. Theorem. Let X,Y be normal compact varieties. If Y satisfies one of the following conditions, then every compact subvariety of \(Sur(X,Y)=\{f\in Hol(X,Y): f\) surjective\(\}\) is contained in some Aut-orbit: (i) Y has non-negative Kodaira dimension. (ii) Y is Moišezon with numerically almost effective canonical sheaf.