An analogue of the Narasimhan-Seshadri theorem in higher dimensions and some applications

Abstract

We prove an analogue in higher dimensions of the classical Narasimhan-Seshadri theorem for strongly stable vector bundles of degree 0 on a smooth projective variety χ with a fixed ample line bundle ⊖. As applications, over fields of characteristic 0, we give a new proof of the main theorem from a recent paper by Balaji and Kollàr ('Holonomy groups of stable vector bundles', Publ. RIMS Kyoto Univ. 44 (2008) 183-211, archiv:math.AG/06001120) and derive an effective version of this theorem; over uncountable fields of positive characteristics, if G is a simple and simply connected algebraic group and the characteristic of the field is bigger than the Coxeter index of G, we prove the existence of strongly stable principal G-bundles on smooth projective surfaces having the holonomy group of the whole of G.