## Tohoku Mathematical Journal 2001 September SECOND SERIES VOL. 53, NO. 3

 Tohoku Math. J. 53 (2001), 337-367

Title PRINCIPAL BUNDLES OVER PROJECTIVE MANIFOLDS WITH PARABOLIC STRUCTURE OVER A DIVISOR

Dedicated to the memory of Krishnamurty Guruprasad

Author Vikraman Balaji, Indranil Biswas and Donihakkalu S. Nagaraj

(Received May 25, 1999, revised January 15, 2001)
Abstract. Principal \$G\$-bundles with parabolic structure over a normal crossing divisor are defined along the line of the interpretation of the usual principal \$G\$-bundles as functors from the category of representations, of the structure group \$G\$, into the category of vector bundles, satisfying certain axioms. Various results on principal bundles are extended to the more general context of principal bundles with parabolic structures, and also to parabolic \$G\$-bundles with Higgs structure. A simple construction of the moduli space of parabolic semistable \$G\$-bundles over a curve is given, where \$G\$ is a semisimple linear algebraic group over \$\boldsymbol{C}\$.

2000 Mathematics Subject Classification. 14F05, 14L30.