Abstract
Abstract In [4], Brown proved that the I-function of a toric fibration lies on the overruled Lagrangian cone of its $g=0$ Gromov–Witten theory, introduced by Coates and Givental [8]. In this paper, we prove the theorem for partial flag-variety fibrations. To do so, we construct new moduli spaces generalising the idea of Ciocan-Fontanine, Kim and Maulik [7].
Highlights
Gromov–Witten theory is a crucial part of one side of mirror symmetry
It can be encoded as a statement about a generating function of Gromov–Witten invariants
The I-function is known to be a counterpart of the J-function in mirror symmetry
Summary
Gromov–Witten theory is a crucial part of one side of mirror symmetry. It can be encoded as a statement about a generating function of Gromov–Witten invariants. From mirror symmetry it follows that the I-function appears as a solution of differential equations which has a beautiful presentation as a hypergeometric series This description can be used in several applications of the study of = 0 Gromov–Witten theory. Inspired by Givental’s idea, CiocanFontanine, Kim and Maulik constructed quasimap moduli spaces for a GIT quotient [7], which suggested a concrete definition of the I-function in greater generality [6]. One advantage of this approach is that one can study the I-function without knowledge of the mirror. The main purpose of this article is to prove the mirror theorem for fibre bundles whose fibre is a flag variety using moduli spaces
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