English

Degenerate complex Monge-Amp\`ere equations over compact K\"ahler manifolds

Differential Geometry 2009-03-24 v3

Abstract

We prove the existence and uniqueness of the solutions of some very general type of degenerate complex Monge-Amp\`ere equations. This type of equations is precisely what is needed in order to construct K\"ahler-Einstein metrics over irreducible singular K\"ahler spaces with ample or trivial canonical sheaf and singular K\"ahler-Einstein metrics over varieties of general type.

Keywords

Cite

@article{arxiv.0710.5109,
  title  = {Degenerate complex Monge-Amp\`ere equations over compact K\"ahler manifolds},
  author = {Jean-Pierre Demailly and Nefton Pali},
  journal= {arXiv preprint arXiv:0710.5109},
  year   = {2009}
}

Comments

The present manuscript expands and completes a paper accepted for publication in the International Journal of Mathematics, which had to be shortened in view of the length of the manuscript and of the demands of referees - in particular it gives more details about the relation with the existing litterature (see Appendix C)

R2 v1 2026-06-21T09:36:54.228Z