Gravitational instantons and K3 surfaces
Gravitational instantons and K3 surfaces

Jeffrey A. Viaclovsky, University of California, Irvine
Fine Hall 314
There are many interesting examples of complete noncompact Ricciflat metrics in dimension 4, which are referred to as ALE, ALF, ALG, ALH gravitational instantons. In this talk, I will describe some examples of these geometries, and another type called ALH_b. All of the above types of gravitational instantons arise as bubbles for sequences of Ricciflat metrics on K3 surfaces, and are therefore important for understanding the behavior of CalabiYau metrics near the boundary of the moduli space. I will describe some general aspects of this type of degeneration, and some recent work on degenerations of Ricciflat metrics on elliptic K3 surfaces in which case ALG bubbles can arise.