| 概要 | We investigate weak BAB conjecture, that is, the boundedness of the anti-canonical
volumes of  -klt log Fano varieties. We prove that weak BAB for Mori fiber spaces
implies weak BAB. Furthermore, we investigate -klt log Fano
3-folds with some Mori fiber space structure, more precisely, with a
del Pezzo fibration structure, or a conic bundle structure over
projective plane. We give a sharp bound for the log anti-canonical
volumes of such pairs. The method is constructing non-klt centers and
using connectedness lemma. |