Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
ASYMPTOTICS OF THE BERGMAN FUNCTION FOR SEMIPOSITIVE HOLOMORPHIC LINE BUNDLES
Koji CHOJoe KAMIMOTOToshihiro NOSE
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2011 Volume 65 Issue 2 Pages 349-382

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Abstract

In this paper, an asymptotic expansion of the Bergman function at a degenerate point is given for high powers of semipositive holomorphic line bundles on compact Kähler manifolds, whose Hermitian metrics have some kind of quasihomogeneous properties. In the sense of pointwise asymptotics, this expansion is a generalization of the expansion of Tian-Zelditch-Catlin-Lu in the positive line bundle case.

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© 2011 Faculty of Mathematics, Kyushu University
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