Scalar-flat Kahler ALE metrics on minimal resolutions

Jeff Viaclovsky, University of Wisconsin
Fine Hall 314

Scalar-flat Kahler ALE surfaces have been studied in a variety of settings since the late 1970s.  All previously known examples have group at infinity either cyclic or contained in SU(2).  I will describe an existence result for scalar-flat Kahler ALE metrics with group at infinity G, where the underlying space is the minimal resolution of C^2/G, for all finite subgroups G of U(2) which act freely on S^3. I will also discuss a non-existence result for Ricci-flat metrics on certain spaces, which is related to a conjecture of Bando-Kasue-Nakajima. If time permits, I will also present some new examples self-dual metrics on connected sums of complex projective planes. This is joint work with Michael Lock.