An ampleness criterion with the extendability of singular positive metrics

Shin ichi Matsumura

doi:10.1007/s00209-012-0995-y

An ampleness criterion with the extendability of singular positive metrics

Shin ichi Matsumura

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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{pipe}_V along a subvariety V ⊂ Xcan 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.

Original language	English
Pages (from-to)	43-54
Number of pages	12
Journal	Mathematische Zeitschrift
Volume	273
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-012-0995-y
Publication status	Published - 2013 Jan 1
Externally published	Yes

Keywords

Ample line bundles
Currents
Psh functions
Singular metrics

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00209-012-0995-y

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AB - 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{pipe}V along a subvariety V ⊂ Xcan 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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KW - Currents

KW - Psh functions

KW - Singular metrics

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ER -

An ampleness criterion with the extendability of singular positive metrics

Abstract

Keywords

ASJC Scopus subject areas

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