# Iterated destabilizing modifications for vector bundles with connection

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00348159
Contributor : Carlos Simpson <>
Submitted on : Wednesday, December 17, 2008 - 11:29:41 PM
Last modification on : Friday, January 12, 2018 - 1:50:44 AM
Long-term archiving on: Tuesday, June 8, 2010 - 5:43:19 PM

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• HAL Id : hal-00348159, version 1
• ARXIV : 0812.3472

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Carlos Simpson. Iterated destabilizing modifications for vector bundles with connection. 2008. ⟨hal-00348159⟩

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