English

The conformal limit for Nakajima quiver varieties

Algebraic Geometry 2026-05-13 v2 Differential Geometry Geometric Topology

Abstract

Inspired by Gaiotto's conformal limit construction for Higgs bundles we define and study a conformal limit construction for Nakajima quiver varieties. We prove that the conformal limit is indeed a limit of a one parameter family of points inside a specified quiver variety and that it gives a biholomorphic map between holomorphic Lagrangian submanifolds foliating two different quiver varieties. In the last part of the paper we discuss the analog of Simpson's conjecture on the completeness of these holomorphic Lagrangian submanifolds.

Keywords

Cite

@article{arxiv.2604.17006,
  title  = {The conformal limit for Nakajima quiver varieties},
  author = {Sotiria Chatzimarkou and Panagiotis Dimakis},
  journal= {arXiv preprint arXiv:2604.17006},
  year   = {2026}
}

Comments

Second draft. Full proof of the Simpson foliation conjecture for quiver varieties added. Various minor changes. Comments welcome!