Opers, Quot-schemes and Frobenius-destabilised vector bundles over curves

Opers, Quot-schemes and Frobenius-destabilised vector bundles over curves

Tue, 10/11/2009
15:45 		Christian Pauly (Montpellier) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Opers, Quot-schemes and Frobenius-destabilised vector bundles over curves
In this talk I will introduce and study opers over a smooth projective curve X defined over a field of positive characteristic. I will describe a bijective correspondence between the set of stable vector bundles E over X such that the pull-back F^*(E) under the Frobenius map F of X has maximal Harder-Narasimhan polygon and the set of opers having zero p-curvature. These sets turn out to be finite, which allows us to derive dimensions of certain Quot-schemes and certain loci of stable Frobenius-destabilized vector bundles over X.