Systematic treatment of non-projective Jeffrey–Kirwan residue arrangements

Develop a systematic procedure for resolving degenerate or non-projective hyperplane arrangements in Jeffrey–Kirwan residue computations, including cases in which the relevant covectors do not lie in a common half-space.

Background

The Jeffrey–Kirwan residue formula requires handling singularities where more than the gauge-group rank of hyperplanes meet and arrangements that may be non-projective. The paper restricts its analysis to cases that can be treated by introducing sufficient equivariant parameters, leaving the general computational problem unresolved.

References

In general, a systematic procedure to resolve this issue is not known to the best of our knowledge.

— Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues  (2501.03365 - Bao et al., 6 Jan 2025) in Section 2, paragraph “The space \(\mathfrak{M}\)”