A Vafa-Intriligator formula for semi-positive quotients of linear spaces

Abstract

We consider genus zero quasimap invariants of smooth projective targets of the form $V//G$, where $V$ is a representation of a reductive group $G$. In particular we consider integrals of cohomology classes arising as characteristic classes of the universal quasimap. In this setting, we provide a way to express the invariants of $V//G$ in terms of invariants of $V//T$, where $T$ is a maximal subtorus of $G$. Using this, we obtain residue formulae for such invariants as conjectured by Kim, Oh, Yoshida and Ueda. Finally, under some positivity assumptions on $V//G$, we prove a Vafa-Intriligator formula for the generating series of such invariants, expressing them as finite sums of explicit contributions.

44 pages, 3 figures. Comments welcome