Collapsing geometry of hyperkaehler four-manifolds

Abstract: This talk focuses on the recent resolution of the following three well-known conjectures in the study of Ricci-flat four manifolds (joint with Song Sun).

(1) Any volume collapsed limit of unit-diameter hyperkaehler metrics on the K3 manifold is isometric to one of the following: the quotient of a flat 3-torus by an involution, a singular special Kaehler metric on the 2-sphere, or the unit interval. (2) Any complete non-compact hyperkaehler 4-manifold with quadratically integrable curvature must have one of the following asymptotic model geometries: ALE, ALF, ALG, ALH, ALG* and ALH*. (3) Any gravitational instanton is holomorphic to an open dense subset of some compact algebraic surface.

With the above classification results, we obtain a rather complete picture of the collapsing geometry of hyperkaehler four manifolds.

Mathematics

Audience: researchers in the topic

Geometry Seminar - University of Florence

Series comments: If you are interested in attending, please send a message to daniele.angella@unifi.it or francesco.pediconi@unifi.it.