Friday, May 11, 2018
3:00 PM -
5:00 PM
Building 15, Room 104
Geometry and Topology Seminar
Geometry of weightless Kapustin-Witten solutions on the plane
The Kapustin-Witten equations are an analogue of the Hitchin equations for a four-manifold. On a compact Kaehler manifold, the solutions are slope-stable Higgs bundles that are Simpson-integrable. On the projective plane, we need the additional data of a parabolic structure along a curve in order to attain a well-defined, nonempty moduli space. By twisting by the divisor of the curve and forgetting the weights, we arrive at a larger moduli space into which the Kapustin-Witten spaces are embedded. We use classical facts about holomorphic bundles on the plane to construct interesting loci within this moduli space.
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