Singularity models of collapsed Ricci flat spaces

Singularity models of collapsed Ricci flat spaces

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Ruobing Zhang, Princeton University
Fine Hall 314

We exhibit some new constructions of collapsed Ricci flat spaces which works for a general context. Such spaces can be decomposed into regular and singular regions in a natural way. Each regular region carries a collapsed fibration structure but curvatures might blow up everywhere. Particularly in dimension 4, the collapsing geometry of the regular region corresponds to the nilpotent Killing structure in the category of collapsing with bounded sectional curvatures due to Cheeger-Fukaya-Gromov. A special example of our construction arises from the codimension-3 collapsed K3 surfaces.