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

Balaji, V. ; Parameswaran, A. J. (2011) An analogue of the Narasimhan-Seshadri theorem in higher dimensions and some applications Journal of Topology, 4 (1). pp. 105-140. ISSN 1753-8416

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Official URL: http://jtopol.oxfordjournals.org/content/4/1/105.s...

Related URL: http://dx.doi.org/10.1112/jtopol/jtq036

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.

Item Type:Article
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ID Code:82820
Deposited On:15 Feb 2012 05:12
Last Modified:22 Jun 2012 19:31

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