HOLOMORPHIC MAPS ONTO KÄHLER MANIFOLDS WITH NON-NEGATIVE KODAIRA DIMENSION

- Journal title : Journal of the Korean Mathematical Society
- Volume 44, Issue 5, 2007, pp.1079-1092
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2007.44.5.1079

Title & Authors

HOLOMORPHIC MAPS ONTO KÄHLER MANIFOLDS WITH NON-NEGATIVE KODAIRA DIMENSION

Hwang, Jun-Muk; Peternell, Thomas;

Hwang, Jun-Muk; Peternell, Thomas;

Abstract

This paper studies the deformation theory of a holomorphic surjective map from a normal compact complex space X to a compact manifold Y. We will show that when the target has non-negative Kodaira dimension, all deformations of surjective holomorphic maps come from automorphisms of an unramified covering of Y and the underlying reduced varieties of associated components of Hol(X, Y) are complex tori. Under the additional assumption that Y is projective algebraic, this was proved in [7]. The proof in [7] uses the algebraicity in an essential way and cannot be generalized directly to the setting. A new ingredient here is a careful study of the infinitesimal deformation of orbits of an action of a complex torus. This study, combined with the result for the algebraic case, gives the proof for the setting.

Keywords

holomorphic maps;complex torus action;

Language

English

Cited by

1.

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