New examples of Collapsed Ricci-flat Spaces

Ruobing Zhang, Stony Brook University
Fine Hall 314

In this talk, we will focus on the construction of new examples of collapsed Ricci-flat spaces. A special case is to construct a family of hyperkähler metrics on a K3 surface such that they are collapsing to a closed interval. Geometrically, the regular collapsing fibers in our example are 3D-Heisenberg (nilpotent) manifolds with almost flat metrics, while the singular collapsing fibers are 3D smooth manifolds which are singular S^1-fibrations over T^2. Compared with the known examples of codimension-1 and codimension-2 collapsing, we will see how such a collapsing phenomenon is related to a general regularity problem.