Gravitational instantons and K3 surfaces

Gravitational instantons and K3 surfaces

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Jeffrey A. Viaclovsky, University of California, Irvine
Fine Hall 314

There are many interesting examples of complete non-compact Ricci-flat 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 Ricci-flat metrics on K3 surfaces, and are therefore important for understanding the behavior of Calabi-Yau 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 Ricci-flat metrics on elliptic K3 surfaces in which case ALG bubbles can arise.