Hyper-Kummer construction

Speaker：Lie Fu (University of Strasbourg)

Time：2026-7-20 9:00

Location：Conference Room S105 at Experiment Building at Haiyun Campus

Abstract:

Classical Kummer construction relates abelian surfaces and K3 surfaces. The hyper-Kummer construction, discovered by Salvatore Floccari, relates in an analogous similar way hyper-Kähler 6-folds of Kummer type and hyper-Kähler 6-folds of K3^[3]-type. I will report a recent joint work with Salvatore Floccari on a systematic study of the hyper-Kummer construction. I will present various relations between the hyper-Kähler 6-folds of Kummer type and the hyper-Kummer 6-folds of K3^[3]-type, on the level of topology, Hodge theory, derived categories, and motives. Time permitting, I will conclude by giving some nice applications on algebraic cycles, e.g. Beauville weak splitting conjecture, Hodge and Tate conjecture, and Kimura-O'Sullivan finite-dimensionality conjecture.