Holomorphic maps onto K\＂ahler manifolds with non-negative Kodaira dimension
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Abstract
This paper studies the deformation theory of a holomorphicsurjective map from a normal compact complex space X to a compactKahler manifold Y. We will show that when the target has non-negativeKodaira dimension, all deformations of surjective holomorphic maps X !Y come from automorphisms of an unramied covering of Y and theunderlying reduced varieties of associated components of Hol(X;Y) arecomplex tori. Under the additional assumption that Y is projective al-gebraic, this was proved in [7]. The proof in [7] uses the algebraicity inan essential way and cannot be generalized directly to the Kahler setting.A new ingredient here is a careful study of the innitesimal deformationof orbits of an action of a complex torus. This study, combined with theresult for the algebraic case, gives the proof for the Kahler setting.
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