Description:

Title: Singular fibers of some minimal abelian fibrations

Abstract: Let f : X -> S be a minimal, flat, and projective degeneration of n-dimensional abelian varieties over a curve S. Then its singular fiber X_s, though not an abelian variety itself, admits a notion of an "abelian variety part". In this talk, I will report my recent result on classifying such singular fibers X_s when it has an (n-1)-dimensional abelian variety part. This generalizes Kodaira's classification of singular fibers in minimal elliptic surfaces, and Matsushita, Hwang, and Oguiso's classification of codimension 1 singular fibers in Lagrangian fibrations.