Conformal blocks, parahoric torsors and Borel-Weil-Bott
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| Format: | Preprint |
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2025
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| _version_ | 1866909940823621632 |
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| author | Balaji, V. Pandey, Y. |
| author_facet | Balaji, V. Pandey, Y. |
| contents | Let $X$ be a smooth projective curve over an algebraically closed field $k$. Let $\mathcal{G}$ be a parahoric group scheme on $X$ as in \cite{pr}. Via the principle of Hecke correspondences, we set-up relationships between the cohomology of lines bundles on various moduli stacks of torsors. This approach gives a proof of \cite[Conjecture 3.7]{pr} for group schemes $\mathcal G$ as above in characteristic zero. This further gives as a consequence, the principle of propagation of vacua. We give a direct proof of the independence of central charge on base points. Projective flatness is recovered as a corollary of Faltings construction of the Hitchin connection. Using C.Teleman's basic results (\cite{bwb}), we deduce the analogous result that cohomology of line bundles on the stack of principal $G$-bundles vanish in all degrees except possibly one. Results on twisted vacua \cite{hongkumar} are obtained as immediate consequences. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_17573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal blocks, parahoric torsors and Borel-Weil-Bott Balaji, V. Pandey, Y. Algebraic Geometry 14F22, 14D23, 14D20 Let $X$ be a smooth projective curve over an algebraically closed field $k$. Let $\mathcal{G}$ be a parahoric group scheme on $X$ as in \cite{pr}. Via the principle of Hecke correspondences, we set-up relationships between the cohomology of lines bundles on various moduli stacks of torsors. This approach gives a proof of \cite[Conjecture 3.7]{pr} for group schemes $\mathcal G$ as above in characteristic zero. This further gives as a consequence, the principle of propagation of vacua. We give a direct proof of the independence of central charge on base points. Projective flatness is recovered as a corollary of Faltings construction of the Hitchin connection. Using C.Teleman's basic results (\cite{bwb}), we deduce the analogous result that cohomology of line bundles on the stack of principal $G$-bundles vanish in all degrees except possibly one. Results on twisted vacua \cite{hongkumar} are obtained as immediate consequences. |
| title | Conformal blocks, parahoric torsors and Borel-Weil-Bott |
| topic | Algebraic Geometry 14F22, 14D23, 14D20 |
| url | https://arxiv.org/abs/2506.17573 |