Moduli spaces of vector bundles on a curve and opers
| Autor: | Biswas, Indranil, Hurtubise, Jacques, Roubtsov, Vladimir |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $X$ be a compact connected Riemann surface of genus $g$, with $g\, \geq\,2$, and let $\xi$ be a holomorphic line bundle on $X$ with $\xi^{\otimes 2}\,=\, {\mathcal O}_X$. Fix a theta characteristic $\mathbb L$ on $X$. Let ${\mathcal M}_X(r,\xi)$ be the moduli space of stable vector bundles $E$ on $X$ of rank $r$ such that $\bigwedge^r E\,=\, \xi$ and $H^0(X,\, E\otimes{\mathbb L})\,=\, 0$. Consider the quotient of ${\mathcal M}_X(r,\xi)$ by the involution given by $E\, \longmapsto\, E^*$. We construct an algebraic morphism from this quotient to the moduli space of ${\rm SL}(r,{\mathbb C})$ opers on $X$. Since $\dim {\mathcal M}_X(r,\xi)$ coincides with the dimension of the moduli space of ${\rm SL}(r,{\mathbb C})$ opers, it is natural to ask about the injectivity and surjectivity of this map. Comment: Final version |
| Databáze: | arXiv |
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