TY - JOUR
T1 - Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle
JF - Differential Geometry and its Applications 29 (2011) 147-153
Y1 - 2011
A1 - Indranil Biswas
A1 - Ugo Bruzzo
PB - Elsevier
UR - http://hdl.handle.net/1963/3830
U1 - 497
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - On semistable principal bundles over complex projective manifolds, II
JF - Geom. Dedicata 146 (2010) 27-41
Y1 - 2010
A1 - Indranil Biswas
A1 - Ugo Bruzzo
AB - 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.
UR - http://hdl.handle.net/1963/3404
U1 - 928
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - On semistable principal bundles over a complex projective manifold
JF - Int. Math. Res. Not. vol. 2008, article ID rnn035
Y1 - 2008
A1 - Indranil Biswas
A1 - Ugo Bruzzo
AB - 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.
PB - Oxford University Press
UR - http://hdl.handle.net/1963/3418
U1 - 917
U2 - Mathematics
U3 - Mathematical Physics
ER -