The London Geometry and Topology Seminar
Many moduli spaces appearing in algebraic geometry and topology admit a symplectic structure on the smooth locus, such as: character varieties and moduli of Higgs bundles on Riemann surfaces, moduli of sheaves on K3 surfaces, and Nakajima quiver varieties. At singularities they are often known to étale-locally have quiver models. This implies geometric properties such as normality and factoriality, or existence of symplectic resolutions. I will explain how this falls under a general framework of moduli of sheaves/modules over 2-Calabi-Yaus. A theorem of Bocklandt-Galluzzi-Vaccarino provides the local model, once one establishes the 2CY property. I will explain a theorem in joint work with Kaplan which carries this out for character varieties of open surfaces, or more generally multiplicative quiver varieties.