Quasiplurisubharmonic Green functions

Abstract

Given a compact Kähler manifold $X$, a quasiplurisubharmonic function is called a Green function with pole at $p\in X$ if its Monge-Ampère 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.

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

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