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arXiv · 1107.3223

An ampleness criterion with the extendability of singular positive metrics

Shin-ichi Matsumura
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Abstract

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 on $L$. 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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Shin-ichi Matsumura. 2011-07-16. An ampleness criterion with the extendability of singular positive metrics. https://arxiv.org/abs/1107.3223

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