Iterated destabilizing modifications for vector bundles with connection

By Carlos Simpson. 2008

51 citations recorded by the source corpus.

Given a vector bundle with integrable connection $(V,\nabla )$ 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 $F^p$ which satisfies Griffiths transversality. The associated graded Higgs bundle is the limit of $(V,t\nabla )$ 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c1469f0975496a92972aef5fa08026829ce3594e

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Betti Geometric Langlands (2016, background): “A more subtle aspect of the Hodge filtration (identified in these terms in [Si2]) is the presence of a distinguished subvariety OpG∨(X) ⊂ ConnG∨(X), the opers of Beilinson-Drinfeld, for which the geometric Langlands conjecture was proved in [BD]: the structure sheaf OOpG∨ (X) corresponds to the D-mo”