Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 3

Special Issue in Honor of Duong H. Phong

Edited by Tristan Collins, Valentino Tosatti, and Ben Weinkove

Positivity of Weil–Petersson currents on canonical models

Pages: 1045 – 1059

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n3.a9


Bin Guo (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.; and Department of Mathematics and Computer Science, Rutgers University, Newark, New Jersey, U.S.A.)

Jian Song (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)


We show that the Weil–Petersson current is a global nonnegative closed $(1,1)$-current in the twisted Kähler–Einstein equation on non-general type canonical models.

The authors’ research was supported in part by National Science Foundation grants DMS- 710500 and DMS-1711439.

Received 7 July 2019

Accepted 7 January 2020

Published 14 June 2021