Intersection theory on singular moduli spaces of vector bundles: a parabolic approach
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912937329819648 |
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| author | Felisetti, Camilla Trapeznikova, Olga |
| author_facet | Felisetti, Camilla Trapeznikova, Olga |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01946 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Intersection theory on singular moduli spaces of vector bundles: a parabolic approach Felisetti, Camilla Trapeznikova, Olga Algebraic Geometry 14D20 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. |
| title | Intersection theory on singular moduli spaces of vector bundles: a parabolic approach |
| topic | Algebraic Geometry 14D20 |
| url | https://arxiv.org/abs/2603.01946 |