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Session S35 - Moduli Spaces in Algebraic Geometry and Applications

Tuesday, July 20, 17:20 ~ 18:00 UTC-3

The Vafa-Witten equations and $T$-branes

Ruxandra Moraru

University of Waterloo, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The Vafa-Witten equations are a higher-dimensional analogue of the Hitchin equations on compact Riemann surfaces for oriented four-manifolds. On a compact complex surface, their solutions are polystable Higgs bundles (with Higgs fields taking values in a vector bundle twisted by the canonical bundle of the surface); T-branes are solutions whose Higgs fields are non-abelian. In this talk, we describe the geometry of T-branes and prove, in particular, that they can only exist on properly elliptic surfaces and surfaces of general type. We also give examples.

Joint work with Fernando Marchesano and Raffaele Savelli.

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