Iterated destabilizing modifications for vector bundles with connection

2008/12/18 by Simpson, Carlos T. · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0812.3472

Abstract

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 F^p 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.

Cited by

• Kodaira-Spencer Map on the Hitchin-Simpson Correspondence
• Frobenius induced morphisms on moduli of sheaves on curves

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