TY - JOUR
T1 - An ampleness criterion with the extendability of singular positive metrics
AU - Matsumura, Shin ichi
PY - 2013/1/1
Y1 - 2013/1/1
N2 - 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.
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.
KW - Ample line bundles
KW - Currents
KW - Psh functions
KW - Singular metrics
UR - http://www.scopus.com/inward/record.url?scp=84872301729&partnerID=8YFLogxK
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U2 - 10.1007/s00209-012-0995-y
DO - 10.1007/s00209-012-0995-y
M3 - Article
AN - SCOPUS:84872301729
SN - 0025-5874
VL - 273
SP - 43
EP - 54
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 1-2
ER -