Stable quasimaps to holomorphic symplectic quotients

TL;DR

This paper investigates the moduli spaces of twisted quasimaps and stable twisted quiver bundles to Nakajima quiver varieties, establishing their symmetric obstruction theories and their equivalence under certain stability conditions, generalizing previous ADHM quiver results.

Contribution

It demonstrates the equivalence of moduli spaces of twisted quasimaps and stable twisted quiver bundles for large stability parameter, extending known results to a broader class of quiver varieties.

Findings

Moduli spaces carry symmetric obstruction theories.

Equivalence of moduli spaces when stability parameter is large.

Generalization of ADHM quiver results to Nakajima quiver varieties.

Abstract

We study the moduli space of twisted quasimaps from a fixed smooth projective curve to a Nakajima's quiver variety and the moduli space of $\delta$-stable framed twisted quiver bundles with moment map relations. We show that they carry symmetric obstruction theories and when $\delta$ is large enough, they exactly coincide. These results generalize works of D.E. Diaconescu about the ADHM quiver, in the framework of the quasimap theory of I. Ciocan-Fontanine, D. Maulik and the author.