Quasimaps to GIT fiber bundles and applications

TL;DR

This paper extends Brown's theorem on the I-function of toric fibrations to partial flag variety fibrations by constructing new moduli spaces, advancing the understanding of Gromov-Witten invariants in these geometries.

Contribution

It introduces new moduli spaces for partial flag varieties and proves the I-function lies on the Lagrangian cone, generalizing previous results to broader classes of fibrations.

Findings

Proved the I-function for partial flag fibrations lies on the Lagrangian cone.

Constructed new moduli spaces generalizing previous models.

Extended Gromov-Witten theory results to new geometric settings.

Abstract

Brown proved that the I-function of a toric fibration lies on the overruled Lagrangian cone of its genus zero Gromov-Witten theory, introduced by Coates and Givental. In this paper, we prove the theorem for partial flag variety fibrations. To do so, we will construct new moduli spaces generalising the idea of Ciocan-Fontanine, Kim and Maulik.