Speaker: Ruobing Zhang, Department of Mathematics, Princeton University
Venue: Tencent Meeting ID: 811 438 125
Abstract:
This talk focuses on the recent resolution of three folklore conjectures in the field (joint with Song Sun).
(1) Any volume collapsed limit of unit-diameter Calabi-Yau metrics on the K3 manifold is isometric to one of the following: a flat 3-torus quotient by revolution, a special Kähler metric on a 2-sphere, and the unit interval.
(2) Any gravitational instanton, as a bubble limit, has one of the six asymptotic model geometries (with optimal asymptotic rates): ALE, ALF, ALG, ALG*, ALH, and ALH*.
(3) Any gravitational instanton can be holomorphically compactified to be an open dense subset of a compact algebraic surface. With the above classification results, we obtain a rather complete picture of degenerating Calabi-Yau manifolds in complex dimension two.
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