On the desingularisation of moduli of principal bundles
Abstract
In \cite{nr} Narasimhan and Ramanan and in \cite{desing}, Seshadri constructed desingularisations of the moduli space $M^{ss}_{_{\text{SL}(2)}}$ of semistable $\SL(2)$-bundles on a smooth projective curve $C$ of genus $g \geq 3$. Seshadri's construction was even modular and canonical. In this paper, we construct a smooth modular compactification of the moduli of stable principal $H$-bundles when $H$ is a simply connected almost simple algebraic group of type ${\tt B}_{_\ell}, {\tt D}_{_\ell}, {\tt G}_{_2}, {\tt F}_{_4}~~or~~{\tt C}_{_3}$. These spaces give canonical desingularisations of the moduli space $M^{ss}_{_H}$ of semistable principal $H$-bundles and thereby, a comprehensive generalisation of \cite{desing}.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.18079
- arXiv:
- arXiv:2407.18079
- Bibcode:
- 2024arXiv240718079B
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Representation Theory