Abstract:The theory of complements was introduced by Shokurov when he investigated log flips on threefolds, which turns out to be a very powerful tool in birational geometry. For a Fano fibration from X to Z with X being $\epsilon$-log canonical, Shokurov proposed a conjecture on the boundedness of klt complements, i.e. the existence of klt n-complements for some bounded natural number n. When...
This workshop focuses on recent progress in the boundedness of log Calabi–Yau fibrations. The central question is: under what conditions does the total space of such a fibration belong to a bounded family? Motivated by this, we investigate fibrations whose bases and general fibers are themselves bounded. We show that, after fixing natural invariants, the total spaces are bounded in codimension...