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 |
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Pages (from-to) | 43-54 |
Number of pages | 12 |
Journal | Mathematische Zeitschrift |
Volume | 273 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 2013 Jan 1 |
Externally published | Yes |
Keywords
- Ample line bundles
- Currents
- Psh functions
- Singular metrics
ASJC Scopus subject areas
- Mathematics(all)