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

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.

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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