Degenerations of Ricci Flat Kahler Metrics under extremal transitions and flops

Xiaochun Rong , Rutgers University
Rutgers - Hill Center, Room 425

We will discuss degeneration of Ricci-flat Kahler metrics on Calabi-Yau manifolds under algebraic geometric surgeries: extremal transitions or flops. We will prove a version of Candelas and de la Ossa's conjecture: Ricci-flat Calabi-Yau manifolds related via extremal transitions and flops can be connected by a path consisting of continuous families of Ricci-flat Calabi-Yau manifolds and a compact metric space in the Gromov-Hausdorff topology. This is joint work with Yuguang Zhang.