Toric pluripotential theory

Dan Coman, Vincent Guedj, Sibel Sahin, Ahmed Zeriahi

Research output: Contribution to journalArticle

Abstract

We study finite energy classes of quasiplurisubharmonic functions in the setting of toric compact Kähler manifolds. We characterize toric quasiplurisubharmonic functions and give necessary and sufficient conditions for them to have finite (weighted) energy, both in terms of the associated convex function in Rn, and through the integrability properties of its Legendre transform. We characterize log-Lipschitz convex functions on the Delzant polytope, showing that they correspond to toric quasiplurisubharmonic functions which satisfy a certain exponential integrability condition. In the particular case of dimension one, those log-Lipschitz convex functions of the polytope correspond to Hölder continuous toric quasisubharmonic functions.

Original languageEnglish (US)
Pages (from-to)215-242
Number of pages28
JournalAnnales Polonici Mathematici
Volume123
Issue number1
DOIs
StatePublished - Jan 1 2019

    Fingerprint

Keywords

  • Ampère operator
  • Complex Monge
  • Delzant polytope
  • Lelong number
  • Quasiplurisubharmonic function
  • Toric manifold

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Coman, D., Guedj, V., Sahin, S., & Zeriahi, A. (2019). Toric pluripotential theory. Annales Polonici Mathematici, 123(1), 215-242. https://doi.org/10.4064/ap180409-3-7