Mathematical Research Letters

Volume 27 (2020)

Number 2

On Fujita’s conjecture for pseudo-effective thresholds

Pages: 377 – 396



Jingjun Han (Beijing International Center for Mathematical Research, Peking University, Beijing, China; and Department of Mathematics, Johns Hopkins University, Baltimore, Maryland, U.S.A.)

Zhan Li (Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, China)


We show Fujita’s spectrum conjecture for $\epsilon \textrm{-}\log$ canonical pairs and Fujita’s log spectrum conjecture for log canonical pairs. Then, we generalize the pseudo-effective threshold of a single divisor to multiple divisors and establish the analogous finiteness and the DCC properties.

This work is partially supported by NSFC Grant No.11601015, and by Postdoctoral Grant No. 2016M591000.

Received 17 August 2018

Accepted 6 July 2019

Published 8 June 2020