Principal bundles over projective manifolds with parabolic structure over a divisor
TLDR
In this article, a simple construction of the moduli space of parabolic semistable principal bundles over a curve is given, where $G$ is a semisimple linear algebraic group over a normal crossing divisor.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 $C$.read more
Citations
More filters
Journal ArticleDOI
On the classification of rank-two representations of quasiprojective fundamental groups
Kevin Corlette,Carlos Simpson +1 more
TL;DR: In this paper, the authors consider a smooth quasiprojective variety over a smooth quadratic variety over the square root of the number of vertices in a graph.
Journal ArticleDOI
Fibrés Paraboliques et Champ des Racines
TL;DR: In this paper, it was shown that the parabolic vector bundles on (X,D) with weights multiples of 1/r (in the sense of Maruyama-Yokogawa) are equivalent to ordinary vector bundles in an orbifold.
Journal ArticleDOI
Moduli of parahoric -torsors on a compact Riemann surface
V. Balaji,C. S. Seshadri +1 more
TL;DR: In this article, the authors introduced the notion of a semistable and stable parahoric torsor under a certain Bruhat-Tits group scheme, and constructed the moduli space of semistably stable G-torsors and identified the underlying topological space of the modulus space with certain spaces of homomorphisms of Fuchsian groups into a maximal compact subgroup.
Journal ArticleDOI
Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants
TL;DR: Ceci as discussed by the authors generalise les result of Agnihotri, du deuxieme auteur et de Belkale sur les valeurs propres d'un produit de matrices unitaires and la cohomologie quantique des grassmanniennes.
Journal ArticleDOI
Katz's middle convolution algorithm
TL;DR: In this paper, an expository account of Katz's middle convolution operation on local systems over local systems is given, and an alternative construction using cyclotomic harmonic bundles is described.
References
More filters
Journal ArticleDOI
The Yang-Mills equations over Riemann surfaces
Michael Atiyah,Raoul Bott +1 more
TL;DR: In this article, the Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory, and the main result is that this is a perfect 9 functional provided due account is taken of its gauge symmetry.
Journal ArticleDOI
Moduli of representations of the fundamental group of a smooth projective variety I
TL;DR: In this article, the authors present a legal opinion on the applicability of commercial or impression systématiques in the context of the agreement of publication mathématique de l'I.H.S.
Proceedings ArticleDOI
Introduction to the Minimal Model Problem
Journal ArticleDOI
Stable and unitary vector bundles on a compact Riemann surface
M. S. Narasimhan,C. S. Seshadri +1 more
TL;DR: In this article, it was shown that on the space of isomorphic classes of unitary vector bundles on X of a given rank, there is a natural structure of a normal projective variety (Theorem 8.1).