Tohoku Mathematical Journal

Principal bundles over projective manifolds with parabolic structure over a divisor

Vikraman Balaji, Indranil Biswas, and Donihakkalu S. Nagaraj

Full-text: Open access

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 $C$.

Article information

Source
Tohoku Math. J. (2) Volume 53, Number 3 (2001), 337-367.

Dates
First available: 3 May 2007

Permanent link to this document
http://projecteuclid.org/euclid.tmj/1178207416

Mathematical Reviews number (MathSciNet)
MR2002h:14026

Digital Object Identifier
doi:10.2748/tmj/1178207416

Zentralblatt MATH identifier
1070.14506

Subjects
Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Secondary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx] 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]

Citation

Balaji, Vikraman; Biswas, Indranil; Nagaraj, Donihakkalu S. Principal bundles over projective manifolds with parabolic structure over a divisor. Tohoku Mathematical Journal 53 (2001), no. 3, 337--367. doi:10.2748/tmj/1178207416. http://projecteuclid.org/euclid.tmj/1178207416.


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