Abstract We study the birational boundedness of special fibers of log Calabi-Yau fibrations and Fano fibrations. We show that for a locally stable family of Fano varieties or polarised log Calabi-Yau pairs over a curve, if the general fiber satisfies some natural boundedness conditions, then every irreducible component of the special fiber is birationally bounded.About the speaker 焦骏鹏,清华...
AbstractIn this talk I will introduce how Prof. Birkar's construction of compact moduli spaces of stable minimal models is used to give a generalization of Shafarevich's program to higher dimensional families with fibers of an arbitrary Kodaira dimension