Subtleties of Quantum Lefshetz without Convexity

Nawaz Sultani; Rachel Webb

paper

Subtleties of Quantum Lefshetz without Convexity

arXiv:2208.08987

Abstract

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

9 pages