An ampleness criterion with the extendability of singular positive metrics

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.

arXiv comment13 pages, to appear in Math. Z. Vol.273, No.1, v2: completely revised version

References in corpus (2)

• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
• Extension of plurisubharmonic functions with growth control