Iterated destabilizing modifications for vector bundles with connection

الأصل · EN

Given a vector bundle with integrable connection (V,∇) on a curve, if V is not itself semistable as a vector bundle then we can iterate a construction involving modification by the destabilizing subobject to obtain a Hodge-like filtration Fᵖ which satisfies Griffiths transversality. The associated graded Higgs bundle is the limit of (V,t∇) under the de Rham to Dolbeault degeneration. We get a stratification of the moduli space of connections, with as minimal stratum the space of opers. The strata have fibrations whose fibers are Lagrangian subspaces of the moduli space.