Subtleties of Quantum Lefshetz without Convexity

TL;DR

This paper investigates the relationship between twisted quasimap invariants and complete intersections in GIT quotients, correcting a previous conjecture and clarifying computational methods in the field.

Contribution

It proves that the $E$-twisted quasimap $I$-function recovers invariants under certain conditions, correcting a conjecture and fixing related computational errors.

Findings

The $E$-twisted quasimap $I$-function recovers invariants if the non-equivariant limit exists.

The paper corrects a conjecture credited to Coates-Corti-Iritani-Tseng.

It provides guidance on fixing computational errors in existing literature.

Abstract

Let $Y\mathord{/\mkern-6mu/}_\theta G$ be a complete intersection in a GIT quotient $X\mathord{/\mkern-6mu/}_\theta G$ cut out by a $G$-representation $E$. We show that the $E$-twisted quasimap $I$-function recovers invariants of $(Y, G, \theta)$ if its nonequivariant limit exists before restriction to $Y\mathord{/\mkern-6mu/}_\theta G$. This corrects a conjecture credited to Coates-Corti-Iritani-Tseng. We explain how to correct computations in the literature based on the faulty conjecture.