8 papers
Automorphism sheaves, spectral covers, and the Kostant and Steinberg sections
Robert Friedman, John W. Morgan
Kostant constructed a section from the adjoint quotient morphism of a simple Lie algebra to the open set of regular elements, and Steinberg constructed such a section for the adjoi…
Holomorphic Principal Bundles Over Elliptic Curves III: Singular Curves and Fibrations
R. Friedman, J. W. Morgan
Let G be a simple and simply connected complex linear algebraic group. In this paper, we discuss the generalization of the parabolic construction of holomorphic principal G-bundles…
Minuscule representations, invariant polynomials, and spectral covers
Robert Friedman, John W. Morgan
Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the a…
Exceptional groups and del Pezzo surfaces
Robert Friedman, John W. Morgan
Given a del Pezzo surface of degree d between 1 and 6, possibly with rational double points, we construct a "tautological" holomorphic G-bundle over X, where G is a reductive group…
On the converse to a theorem of Atiyah and Bott
Robert Friedman, John W. Morgan
Let G be a complex reductive group and let C be a smooth curve of genus at least one. We prove a converse to a theorem of Atiyah-Bott concerning the stratification of the space of…
Holomorphic Principal Bundles Over Elliptic Curves II: The Parabolic Construction
Robert Friedman, John W. Morgan
This paper continues the study of holomorphic semistable principal G-bundles over an elliptic curve. In this paper, the moduli space of all such bundles is constructed by consideri…