On the desingularisation of moduli of principal bundles

In \cite{nr} Narasimhan and Ramanan and in \cite{desing}, Seshadri constructed desingularisations of the moduli space $M_{{}_{\text{SL}(2)}}^{ss}$ of semistable $\text{SL}(2)$-bundles on a smooth projective curve $C$ of genus $g\ge 3$. 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 ${\mathtt{B}}_{{}_{\mathrm{\ell }}},{\mathtt{D}}_{{}_{\mathrm{\ell }}},{\mathtt{G}}_{{}_2},{\mathtt{F}}_{{}_4}or{\mathtt{C}}_{{}_3}$. These spaces give canonical desingularisations of the moduli space $M_{{}_H}^{ss}$ of semistable principal $H$-bundles and thereby, a comprehensive generalisation of \cite{desing}.