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}.