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Higgs bundles, Harmonic Maps and Twistor lines
24.1.2019, 16:15 - 17:15
Speaker:Markus Röser, Universität Hamburg, Fachbereich Mathematik
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerGras Geo Map
Organizer:Mathematisches Institut
The moduli space of Higgs bundles on a Riemann surface is a (usually singular) hyperkähler manifold that plays a prominent role in many areas of mathematics and mathematical physics. We will review the non-abelian Hodge theorem which gives a correspondence between Higgs bundles and harmonic metrics and interpret it in terms of the hyperkähler geometry of the moduli space. Using twistor theory, we may view a harmonic metric as a real holomorphic section of the twistor fibration associated with the moduli space. Our main result is the existence of holomorphic sections that cannot be obtained from harmonic metrics, although they obey the same reality condition. This answers a question by Carlos Simpson.
This is joint work with Florian Beck, Indranil Biswas and Sebastian Heller.
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