Towards a mirror theorem for GLSMs

Abstract We propose a method for computing generating functions of genus-zero invariants of a gauged linear sigma model (GLSM) left parenthesis upper V comma upper G comma theta comma w right parenthesis ( V , G , θ , w ) $(V, G, \theta, w)$ . We show that certain derivatives of I -functions of quasimap invariants of left bracket upper V slash slash Subscript theta Baseline upper G right bracket [ V / / θ G ] $[V\mathbin{/\mkern-6mu/}_\theta G]$ produce I -functions (appropriately defined) of the GLSM. When G is an algebraic torus, we obtain an explicit formula for an I -function, and check that it agrees with previously computed I -functions in known special cases. Our approach is based on a new construction of these invariants that applies whenever the evaluation maps from the moduli space are proper, and includes insertions from light marked points, which may collide with each other and with basepoints.