Extension of twisted Hodge metrics for Kähler morphisms

Christophe Mourougane Campus de Beaulieu Shigeharu Takayama University of Tokyo

Differential Geometry mathscidoc:1609.10135

Journal of Differential Geometry, 83, (1), 131-161, 2009
Let f : X .仺 Y be a holomorphic map of complex manifolds, which is proper, K丯ahler, and surjective with connected fibers, and which is smooth over Y \ Z the complement of an analytic subset Z. Let E be a Nakano semi-positive vector bundle on X. In our previous paper, we discussed the Nakano semi-positivity of Rqf(KX/Y . E) for q . 0 with respect to the so-called Hodge metric, when the map f is smooth. Here we discuss the extension of the induced metric on the tautological line bundle O(1) on the projective space bundle P(Rqf(KX/Y . E)) 乬over Y \ Z乭 as a singular Hermitian metric with semi-positive curvature 乬over Y 乭. As a particular consequence, if Y is projective, Rqf(KX/Y . E) is weakly positive over Y \ Z in the sense of Viehweg.
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@inproceedings{christophe2009extension,
  title={Extension of twisted Hodge metrics for Kähler morphisms},
  author={Christophe Mourougane, and Shigeharu Takayama},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911195337294733792},
  booktitle={Journal of Differential Geometry},
  volume={83},
  number={1},
  pages={131-161},
  year={2009},
}
Christophe Mourougane, and Shigeharu Takayama. Extension of twisted Hodge metrics for Kähler morphisms. 2009. Vol. 83. In Journal of Differential Geometry. pp.131-161. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911195337294733792.
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