Parabolic Pluripotential Theory

Introduction

The goal of this project is to develop a parabolic pluripotential theory motivated by the Minimal Model Program (MMP), whose aim is the (birational) classification of projective manifolds. Inspired by the celebrated work of Birkar-Cascini-Hacon-Mckernan which showed the existence of minimal models for a large class of varieties called varieties of general type, Song and Tian have proposed an analytic analogue making use of the Kähler-Ricci flow. As the models involved in this program are necessarily singular, one is lead to develop a theory of weak Monge-Ampere flows. The first steps of a parabolic pluripotential theory have been built by Guedj-Lu-Zeriahi, allowing one to treat Kawamata log terminal singularities. In this project we aim at developing this theory further, extending it to the most general singularities encountered in the MMP, and studying the geometric convergence of the Monge-Ampère flows.


Members

  1. Quang-Tuan Dang: Ph.D student supervised by Vincent Guedj and Chinh H. Lu
  2. Alix Deruelle: Maître de Conférences, Sorbonne Université
  3. Eleonora Di Nezza: Maître de Conférences, Sorbonne Université, Professeur Monge Ecole Polytechnique
  4. Vincent Guedj: Professeur, Université Paul Sabatier
  5. Chinh H. Lu (PI): Maître de Conférences, Université Paris-Saclay



Preprints and Publications

  1. V. Guedj, C.H. Lu, Quasi-plurisubharmonic envelopes 3: Solving Monge-Ampère equations on hermitian manifolds, with V. Guedj, preprint arXiv:2107.01938.
  2. V. Guedj, C.H. Lu, Quasi-plurisubharmonic envelopes 2: Bounds on Monge-Ampère volumes, with V. Guedj, preprint arXiv:2106.04272.
  3. V. Guedj, C.H. Lu, Quasi-plurisubharmonic envelopes 1: Uniform estimates on Kähler manifolds, with V. Guedj, preprint arXiv:2106.04273.
  4. Q.T. Dang, Pluripotential Monge-Ampère flows in big cohomology class, preprint arXiv:2102.05189.
  5. Q.T. Dang, Continuity of Monge-Ampère potentials in big cohomology classes, preprint arXiv:2102.02704.



Logo
Département de Mathématiques
, Université Paris-Saclay, Bât. 307, F-91405 Orsay Cedex ,France
Last updated on 06 July 2021.