Quasiplurisubharmonic Green functions

Dan Coman; Vincent Guedj

doi:10.1016/j.matpur.2009.05.010

paper

Quasiplurisubharmonic Green functions

arXiv:0907.4449 · doi:10.1016/j.matpur.2009.05.010

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