Ching-Jui Lai, Anticanonical Volume of Singular Fano Threefolds

The set of canonical Fano threefolds form a bounded family by results of Kawamata, Mori-Miyaoka-Kollar-Tagaki, and in a much more general setting by Birkar. In particular, the anticaonical volume –K_X³ is bounded. An optimal lower bound is 1/330 by the work of Chen-Chen. In this talk, we discuss the problem of identifying an optimal upper bound of –K_X³.