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 \(M^{ss}_{_{\text{SL}(2)}}\) 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}.