Quasiplurisubharmonic Green functions

Details Quasiplurisubharmonic Green functions Quasiplurisubharmonic Green functions

2009-07-25

arxiv.org/abs/0907.4449v1

Mathematics

Complex Variables

23 pages; to appear in Journal de Mathematiques Pures et Appliquees

Scientific paper

10.1016/j.matpur.2009.05.010

Given a compact K\"ahler manifold $X$, a quasiplurisubharmonic function is
called a Green function with pole at $p\in X$ if its Monge-Amp\`ere measure is
supported at $p$. We study in this paper the existence and properties of such
functions, in connection to their singularity at $p$. A full characterization
is obtained in concrete cases, such as (multi)projective spaces.

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