Subtleties of Quantum Lefshetz without Convexity

preprint2022arXivOpen access

Abstract

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

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