English

A Vafa-Intriligator formula for semi-positive quotients of linear spaces

Algebraic Geometry 2025-05-26 v1

Abstract

We consider genus zero quasimap invariants of smooth projective targets of the form V/ ⁣/GV/\!/G, where VV is a representation of a reductive group GG. In particular we consider integrals of cohomology classes arising as characteristic classes of the universal quasimap. In this setting, we provide a way to express the invariants of V/ ⁣/GV/\!/G in terms of invariants of V/ ⁣/TV/\!/T, where TT is a maximal subtorus of GG. Using this, we obtain residue formulae for such invariants as conjectured by Kim, Oh, Yoshida and Ueda. Finally, under some positivity assumptions on V/ ⁣/GV/\!/G, we prove a Vafa-Intriligator formula for the generating series of such invariants, expressing them as finite sums of explicit contributions.

Keywords

Cite

@article{arxiv.2505.17845,
  title  = {A Vafa-Intriligator formula for semi-positive quotients of linear spaces},
  author = {Riccardo Ontani},
  journal= {arXiv preprint arXiv:2505.17845},
  year   = {2025}
}

Comments

44 pages, 3 figures. Comments welcome