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Differential Geometry Seminar
On the differential geometry of variations of stability for moduli of parabolic Higgs bundles
On the differential geometry of variations of stability for moduli of parabolic Higgs bundles
演讲者
Claudio Meneses
时间
2025年10月14日 15:00 至 16:00
地点
A7-201
线上
Zoom 388 528 9728
(BIMSA)
摘要
An interesting feature of moduli spaces of stable parabolic Higgs bundles on compact Riemann surfaces is that they determine an infinite series of families of hyper-Kähler metrics, in part coming from the dependence of the former on choices of stability parameters. Although the wall-crossing phenomena associated with such dependence is well understood as a problem in birational geometry, the analogous differential-geometric problem for the hyper-Kähler structure is still outstanding. Due to a theorem independently proved by Feix and Kaledin, this problem can be reduced to a simpler one on a special irreducible component of their nilpotent cone, namely the moduli spaces of stable parabolic bundles.
In this talk I will discuss results on the variation problem in the special case of genus 0. A special feature of this case is that in particular it accounts for all examples in the minimal dimension 2, and these have been conjectured to correspond to all families of gravitational instantons of type ALG.