Intersection theory on singular moduli spaces of vector bundles: a parabolic approach

Camilla Felisetti; Olga Trapeznikova

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arXiv · 2603.01946

Intersection theory on singular moduli spaces of vector bundles: a parabolic approach

Camilla Felisetti·Olga Trapeznikova

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Abstract

We present explicit formulas for the intersection pairing in the intersection cohomology of the moduli space $M_0(r)$ of rank-$r$, degree-$0$ semistable bundles on a Riemann surface. The key idea is to realize this intersection cohomology as a canonical subspace of the cohomology of a smooth moduli space of parabolic bundles, where the pairing can be computed via the Hecke correspondence and the Jeffrey-Kirwan iterated residue formulas. This approach provides a simpler alternative to the blow-up construction of Jeffrey-Kirwan-Kiem-Woolf, yielding formulas for the intersection pairing on $M_0(r)$, for arbitrary $r$, with a clear geometric interpretation.

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Camilla Felisetti, Olga Trapeznikova. 2026-03-02. Intersection theory on singular moduli spaces of vector bundles: a parabolic approach. https://arxiv.org/abs/2603.01946

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