On Vafa-Witten equations over Kaehler manifolds

Abstract: I will talk about some analytic properties of solutions to the Vafa-Witten equations over compact Kaehler manifolds. Simple obstructions to the existence of nontrivial solutions are identified. The gauge theoretical compactness for the C^* invariant locus of the moduli space behaves similarly as the Hermitian-Yang-Mills connections. More generally, this holds for solutions with uniformly bounded spectral covers such as nilpotent solutions. When spectral covers are unbounded, we manage to take limits of the renormalized Higgs fields which are intrinsically characterized by the convergence of the associated spectral covers. This gives a simpler proof for Taubes’ results on rank two solutions over Kaehler surfaces together with a new complex geometric interpretation.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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