Quasiplurisubharmonic Green functions

Dan Coman; Vincent Guedj

doi:10.1016/j.matpur.2009.05.010

Quasiplurisubharmonic Green functions

Complex Variables 2009-07-28 v1 Algebraic Geometry

Authors: Dan Coman , Vincent Guedj

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Abstract

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.

Keywords

harmonic functions

Cite

@article{arxiv.0907.4449,
  title  = {Quasiplurisubharmonic Green functions},
  author = {Dan Coman and Vincent Guedj},
  journal= {arXiv preprint arXiv:0907.4449},
  year   = {2009}
}

Comments

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

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