Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into ℙⁿ(ℂ) intersecting hypersurfaces

Ru, Min; Sogome, Suraizou

doi:10.1090/S0002-9947-2011-05512-1

Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into $\mathbb {P}^n(\mathbb {C})$ intersecting hypersurfaces
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by Min Ru and Suraizou Sogome PDF

Trans. Amer. Math. Soc. 364 (2012), 1145-1162 Request permission

Abstract:

In this paper, we establish a non-integrated defect relation for a meromorphic map of a complete Kähler manifold whose universal covering is biholomorphic to a ball in $\mathbb {C}^m$ into $\mathbb {P}^n(\mathbb {C})$ intersecting hypersurfaces in general position, as well as an application to the Gauss map of a closed regular submanifold of $\mathbb {C}^m$. The result provides a complement to the recent result of Ru (2004) on a defect relation for meromorphic mappings from $\mathbb {C}^m$ into $\mathbb {P}^n(\mathbb {C})$ intersecting hypersurfaces in general position.

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