An ampleness criterion with the extendability of singular positive metrics

Details An ampleness criterion with the extendability of singular positive metrics An ampleness criterion with the extendability of singular positive metrics

2011-07-16

arxiv.org/abs/1107.3223v1

Mathematics

Complex Variables

13 pages

Scientific paper

Coman, Guedj and Zeriahi proved that, for an ample line bundle $L$ on a projective manifold $X$, any singular positive metric on the line bundle $L|_{V}$ along a subvariety $V \subset X$ can be extended to a global singular positive metric of $L$. In this paper, we prove that the extendability of singular positive metrics on a line bundle along a subvariety implies the ampleness of the line bundle.

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