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Moduli varieties of real and quaternionic bundles over a curve

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Florent Schaffhauser
Mon, 2010-04-19 15:00 - 16:00
MPIM Lecture Hall
Parent event: 
Topics in Topology

We examine the moduli problem for real and quaternionic vector bundles over a curve, and we give a gauge-theoretic construction of would-be moduli varieties for such bundles. These moduli varieties are irreducible subsets of real points inside a complex projective variety. We relate our point of view to previous work by Biswas, Huisman and Hurtubise, and we use this to study Gal(C/R)-actions on moduli varieties of semistable holomorphic bundles over a complex curve with a given real structure. We show in particular a Harnack-type theorem, bounding the number of connected components of the fixed-point set of those actions by $2^g +1$, where g is the genus of the curve. Moreover, we show that any two such connected components are homeomorphic.

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