Mathematics

Nested Hilbert schemes of points and curves on smooth projective surfaces carry interesting quantities for both geometry and physics. Their virtual fundamental classes have been shown to recover both the virtual classes of SW and reduced stable pair theories, while their obstruction theories can be used to obtain information about VW and reduced DT invariants. We show that the effective SUSY theory of a certain surface defect gives rise to a quiver GLSM which, in a particular case, models punctual nested Hilbert schemes on the complex plane. We will show how the partition function of such a theory naturally computes certain virtual invariants of these moduli spaces and how these results relate to a conjecture of Hausel, Letellier and Rodriguez-Villegas about the cohomology of character varieties.