Communications in Analysis and Geometry

Volume 29 (2021)

Number 7

Boundedness of anti-canonical volumes of singular $\operatorname{log}$ Fano threefolds

Pages: 1571 – 1596



Chen Jiang (Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China)


We prove the Weak Borisov–Alexeev–Borisov Conjecture in dimension three which states that the anti-canonical volume of an $\epsilon$‑$\operatorname{klt}$ $\operatorname{log}$ Fano pair of dimension three is bounded from above.

The author was supported by Grant-in-Aid for JSPS Fellows (KAKENHI No. 25-6549) and Program for Leading Graduate Schools, MEXT, Japan.

Received 18 May 2017

Accepted 21 March 2019

Published 17 May 2022