Virtual Jeffrey--Kirwan localisation

Riccardo Ontani; Richard P. Thomas

Virtual Jeffrey--Kirwan localisation

Algebraic Geometry 2026-07-06 v1 Symplectic Geometry

Authors: Riccardo Ontani , Richard P. Thomas

Abstract

We express integrals over virtual cycles of GIT quotients $X/\!\!/G$ in terms of integrals over virtual cycles of fixed loci $X^T$ . The results hold for both perfect obstruction theories and $(-2)$ -shifted symplectic structures, in cohomology and in $K$ -theory, and for noncompact Deligne-Mumford stacks acted on by a reductive group with compact quotient.

Cite

@article{arxiv.2607.05575,
  title  = {Virtual Jeffrey--Kirwan localisation},
  author = {Riccardo Ontani and Richard P. Thomas},
  journal= {arXiv preprint arXiv:2607.05575},
  year   = {2026}
}

Comments

8 figures, 69 pages