On quasimap invariants of moduli spaces of Higgs bundles
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910725502402560 |
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| author | Nesterov, Denis |
| author_facet | Nesterov, Denis |
| contents | We compute odd-degree genus 1 quasimap (and Gromov--Witten) invariants of moduli spaces of Higgs $\mathrm{SL}_2$-bundles on a curve of genus $g\geq2$. We also compute certain invariants for all prime ranks. This proves some parts of author's conjectures on quasimap invariants of moduli spaces of Higgs bundles. More generally, our methods provide a computation scheme for genus 1 quasimap (and Gromov--Witten) invariants in the case when degrees of maps are coprime to the rank. This requires a careful analysis of the localisation formula for certain Quot schemes parametrising higher-rank quotients on an elliptic curve. Invariants for degrees which are not coprime to the rank exhibit a very different structure for a reason that we explain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15624 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On quasimap invariants of moduli spaces of Higgs bundles Nesterov, Denis Algebraic Geometry We compute odd-degree genus 1 quasimap (and Gromov--Witten) invariants of moduli spaces of Higgs $\mathrm{SL}_2$-bundles on a curve of genus $g\geq2$. We also compute certain invariants for all prime ranks. This proves some parts of author's conjectures on quasimap invariants of moduli spaces of Higgs bundles. More generally, our methods provide a computation scheme for genus 1 quasimap (and Gromov--Witten) invariants in the case when degrees of maps are coprime to the rank. This requires a careful analysis of the localisation formula for certain Quot schemes parametrising higher-rank quotients on an elliptic curve. Invariants for degrees which are not coprime to the rank exhibit a very different structure for a reason that we explain. |
| title | On quasimap invariants of moduli spaces of Higgs bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2306.15624 |