PARAPLUI

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 Kaehler-Ricci flow. As the models involved in this program are necessarily singular, one is lead to develop a theory of weak Monge-Ampère 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.