A. J. Parameswaran

Monodromy group for a strongly semistable principal bundle over a curve

Let X be a geometrically irreducible smooth projective curve defined over a field k. Assume that X has a k-rational point; fix a k-rational point x e X. From these data we construct an affine group scheme X defined over the field k as well as a principal X-bundle S1755069607000151inline1 over the curve X. The group scheme X is given by a xs0211A-graded neutral Tannakian category built out of all strongly semistable vector bundles over X. The principal bundle S1755069607000151inline1 is tautological. Let G be a linear algebraic group, defined over k, that does not admit any nontrivial character which is trivial on the connected component, containing the identity element, of the reduced center of G. Let E G be a strongly semistable principal G-bundle over X. We associate to E G a group scheme M defined over k, which we call the monodromy group scheme of E G , and a principal M-bundle E M over X, which we call the monodromy bundle of E G . The group scheme M is canonically a quotient of X, and E M is the extension of structure group of S1755069607000151inline1. The group scheme M is also canonically embedded in the fiber Ad(E G ) x over x of the adjoint bundle.

A splitting theorem for good complexifications@@@Un théorème de décomposition pour les bonnes complexifications

The purpose of this paper is to produce restrictions on fundamental groups of manifolds admitting good complexifications by proving the following Cheeger-Gromoll type splitting theorem: Any closed manifold

On the geometry of regular maps from a quasi-projective surface to a curve

M

Nef cone of flag bundles over a curve

admitting a good complexification has a finite-sheeted regular covering

Thom irregularity and Milnor tube fibrations

M_1

On the equivariant reduction of structure group of a principal bundle to a Levi subgroup

such that

A criterion for the strongly semistable principal bundles over a curve in positive characteristic

M_1

Hitchin pairs on an integral curve

admits a fiber bundle structure with base

Monodromy group for a strongly semistable principal bundle over a curve, II

(S^1)^k

Picard Bundles and Brill–Noether Loci in the Compactified Jacobian of a Nodal Curve

and fiber