Boundedness of anti-canonical volumes of singular log Fano threefolds

Abstract

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

20 pages. Comments are welcome; v2: slightly modified; v3: 19 pages, proof slightly modified

References in corpus (2)

• Boundedness of log terminal Fano pairs of bounded index
• The degree of Q-Fano threefolds

Cited by in corpus (1)

• An effective upper bound for anti-canonical volumes of singular Fano threefolds