Geometry of weightless Kapustin-Witten solutions on the plane

Steven Rayan (University of Saskatchewan)

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.