An ampleness criterion with the extendability of singular positive metrics

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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{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 languageEnglish
Pages (from-to)43-54
Number of pages12
JournalMathematische Zeitschrift
Volume273
Issue number1-2
DOIs
Publication statusPublished - 2013 Jan 1
Externally publishedYes

Keywords

  • Ample line bundles
  • Currents
  • Psh functions
  • Singular metrics

ASJC Scopus subject areas

  • Mathematics(all)

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