English

Quasi-polynomials and the singular $[Q,R]=0$ theorem

Symplectic Geometry 2019-11-19 v2

Abstract

In this short note we revisit the `shift-desingularization' version of the [Q,R]=0[Q,R]=0 theorem for possibly singular symplectic quotients. We take as starting point an elegant proof due to Szenes-Vergne of the quasi-polynomial behavior of the multiplicity as a function of the tensor power of the prequantum line bundle. We use the Berline-Vergne index formula and the stationary phase expansion to compute the quasi-polynomial, adapting an early approach of Meinrenken.

Keywords

Cite

@article{arxiv.1907.06113,
  title  = {Quasi-polynomials and the singular $[Q,R]=0$ theorem},
  author = {Yiannis Loizides},
  journal= {arXiv preprint arXiv:1907.06113},
  year   = {2019}
}
R2 v1 2026-06-23T10:20:20.948Z