Pluricanonical fibrations of compact complex manifolds

A pluricanonical fibration of a compact complex manifold is a meromorphic map defined by a sufficiently large and divisible multiple of its canonical class. For a projective variety, a theorem due to P. Deligne and K. Ueno asserts that the image of the automorphism group of the variety in the automorphism group of the base of its pluricanonical fibration is finite. I will tell about an analog of this result for compact complex manifolds of dimension $N$ and Kodaira dimension $N-1$. The talk is based on a joint work with K. Loginov.