%0 Journal Article
%J Differential Geometry and its Applications 29 (2011) 147-153
%D 2011
%T Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle
%A Indranil Biswas
%A Ugo Bruzzo
%B Differential Geometry and its Applications 29 (2011) 147-153
%I Elsevier
%G en_US
%U http://hdl.handle.net/1963/3830
%1 497
%2 Mathematics
%3 Mathematical Physics
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%R 10.1016/j.difgeo.2011.02.001
%0 Journal Article
%J Geom. Dedicata 146 (2010) 27-41
%D 2010
%T On semistable principal bundles over complex projective manifolds, II
%A Indranil Biswas
%A Ugo Bruzzo
%X Let (X, \\\\omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.
%B Geom. Dedicata 146 (2010) 27-41
%G en_US
%U http://hdl.handle.net/1963/3404
%1 928
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-31T11:15:29Z\\nNo. of bitstreams: 1\\nbiswas-bruzzo-2.pdf: 216946 bytes, checksum: 21a4d096140b009d34e486648fe1a555 (MD5)
%R 10.1007/s10711-009-9424-8
%0 Journal Article
%J Int. Math. Res. Not. vol. 2008, article ID rnn035
%D 2008
%T On semistable principal bundles over a complex projective manifold
%A Indranil Biswas
%A Ugo Bruzzo
%X Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \\\\chi of P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold M is semistable and the second Chern class of its adjoint bundle vanishes in rational cohomology if and only if the line bundle over E/P defined by \\\\chi is numerically effective. Similar results remain valid for principal bundles with a reductive linear algebraic group as the structure group. These generalize an earlier work of Y. Miyaoka where he gave a characterization of semistable vector bundles over a smooth projective curve. Using these characterizations one can also produce similar criteria for the semistability of parabolic principal bundles over a compact Riemann surface.
%B Int. Math. Res. Not. vol. 2008, article ID rnn035
%I Oxford University Press
%G en_US
%U http://hdl.handle.net/1963/3418
%1 917
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-12T09:53:34Z\\nNo. of bitstreams: 1\\n0803.4042v1.pdf: 273878 bytes, checksum: 8f729aa65d9cebf234016c17cacfedbc (MD5)
%R 10.1093/imrn/rnn035