Semistable Higgs bundles of small ranks are strongly Higgs semistable

2013/11/11 by Guitang Lan, Mao Sheng, Lan, Guitang +5
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.1311.2405

7 pages

arxiv created 2013/11/11 · openalex publication_date 2013/11/11 · arxiv updated 2013/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a proof of the conjecture that a semistable Higgs bundle is strongly Higgs semistable in the case of small ranks, based upon the fact that there exists a gr-semistable Griffiths-transverse filtration on a ∇-invariant semistable vector bundle. The latter is a generalization of a result of Carlos Simpson.

Citations

• Semistable Higgs bundles and representations of algebraic fundamental groups: Positive characteristic case

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