Differential Geometry and Physics Seminar

Speaker: François Greer, MSU

Title: Boundedness for K-trivial varieties with fibrations

Abstract: According to the Beauville-Bogomolov decomposition theorem, any smooth K-trivial variety admits a finite cover by a product of (1) abelian varieties, (2) strict Calabi-Yau varieties, and (3) irreducible holomorphic symplectic varieties (IHSV). In a fixed dimension, all abelian varieties are diffeomorphic, and indeed deformation equivalent through non-algebraic complex tori. The corresponding question remains largely open for cases (2) and (3). If we assume that a variety of class (2) or (3) admits a non-trivial fibration structure, then much more can be shown. In particular, fibered Calabi-Yau threefolds have bounded moduli problem, and IHSV of a fixed dimension with a Lagrangian fibration have bounded moduli. This is based on joint work with Engel, Filipazzi, Mauri, and Svaldi.