A New Gauge-Theoretic Construction of 4-Dimensional Hyperkähler ALE Spaces

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

Non-compact hyperkähler spaces arise frequently in gauge theory. The 4-dimensional hyperkähler ALE spaces are a special class of non-compact hyperkähler spaces. They are in one-to-one correspondence with the finite subgroups of SU(2) and have interesting connections with representation theory and singularity theory, captured by the McKay Correspondence.

In this talk, we first review the finite-dimensional construction of 4-dimensional hyperkähler ALE spaces given by Peter Kronheimer in his PhD thesis. Then we give a new gauge theoretic construction of these spaces.