Tautological algebra of the moduli stack of semistable bundles of rank 2 on a general curve
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| Format: | Preprint |
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2020
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| _version_ | 1866911305377513472 |
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| author | Gangopadhyay, Chandranandan Iyer, Jaya NN Mukherjee, Arijit |
| author_facet | Gangopadhyay, Chandranandan Iyer, Jaya NN Mukherjee, Arijit |
| contents | Our aim is to determine the tautological algebra generated by the cohomology classes of the Brill-Noether loci in the rational cohomology of the moduli stack $\mathcal{U}_C(n,d)$ of semistable bundles of rank $n$ and degree $d$. We show that for a general smooth projective curve $C$ of genus $g\geq 2$, $d=2g-2$, the tautological algebra of $ \mathcal{U}_C(2,2g-2)$ (resp. the moduli stack $\mathcal{SU}_C(2,\mathcal{L})$ of semistable bundles of rank $2$ and determinant $\mathcal{L}$ with $°(\mathcal{L})=2g-2$) is generated by the divisor classes (resp. the class of the Theta divisor $Θ$). This is previously known in rank one situation, called the (classical) Porteous formula. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2002_00568 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Tautological algebra of the moduli stack of semistable bundles of rank 2 on a general curve Gangopadhyay, Chandranandan Iyer, Jaya NN Mukherjee, Arijit Algebraic Geometry K-Theory and Homology 14D20, 14D23, 14H40, 14H51, 14H60 Our aim is to determine the tautological algebra generated by the cohomology classes of the Brill-Noether loci in the rational cohomology of the moduli stack $\mathcal{U}_C(n,d)$ of semistable bundles of rank $n$ and degree $d$. We show that for a general smooth projective curve $C$ of genus $g\geq 2$, $d=2g-2$, the tautological algebra of $ \mathcal{U}_C(2,2g-2)$ (resp. the moduli stack $\mathcal{SU}_C(2,\mathcal{L})$ of semistable bundles of rank $2$ and determinant $\mathcal{L}$ with $°(\mathcal{L})=2g-2$) is generated by the divisor classes (resp. the class of the Theta divisor $Θ$). This is previously known in rank one situation, called the (classical) Porteous formula. |
| title | Tautological algebra of the moduli stack of semistable bundles of rank 2 on a general curve |
| topic | Algebraic Geometry K-Theory and Homology 14D20, 14D23, 14H40, 14H51, 14H60 |
| url | https://arxiv.org/abs/2002.00568 |