## View abstract

### 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. document.getElementById('cloak917eca83f17f4f76f0b11d5db8a8a0f8').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy917eca83f17f4f76f0b11d5db8a8a0f8 = 'm&#111;r&#97;r&#117;' + '&#64;'; addy917eca83f17f4f76f0b11d5db8a8a0f8 = addy917eca83f17f4f76f0b11d5db8a8a0f8 + '&#117;w&#97;t&#101;rl&#111;&#111;' + '&#46;' + 'c&#97;'; var addy_text917eca83f17f4f76f0b11d5db8a8a0f8 = 'm&#111;r&#97;r&#117;' + '&#64;' + '&#117;w&#97;t&#101;rl&#111;&#111;' + '&#46;' + 'c&#97;';document.getElementById('cloak917eca83f17f4f76f0b11d5db8a8a0f8').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy917eca83f17f4f76f0b11d5db8a8a0f8 + '\'>'+addy_text917eca83f17f4f76f0b11d5db8a8a0f8+'<\/a>';

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.