On the desingularisation of moduli of principal bundles

In {nr} Narasimhan and Ramanan and in {desing}, Seshadri constructed desingularisations of the moduli space Mˢˢ_SL(2) of semistable (2)-bundles on a smooth projective curve C of genus g ≥ 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 B_, D_, G₂, F₄~~or~~ C₃. These spaces give canonical desingularisations of the moduli space MˢˢH of semistable principal H-bundles and thereby, a comprehensive generalisation of {desing}.