Lefschetz principle-type theorems for curve semistable Higgs sheaves and applications to elliptic surfaces

2024/11/30 by Armando Capasso, Capasso, Armando
Mathematics · #14A15 #14F06 #14H45 #14J60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2412.00439

openalex publication_date 2024/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I prove "Lefschetz principle"-type theorems for semistable and curve semistable Higgs sheaves on smooth projective varieties defined over an algebraically closed field of characteristic 0. These theorems are applied to reduce a conjecture, about curve semistable Higgs bundles, from the previous general setting to the complex case. Since this conjecture is equivalent to vanishing of Chern classes of H-nflat Higgs bundles, I consider these last ones over elliptic surfaces. I reduce one more time the conjecture to nilpotent, H-nflat Higgs bundles, and I prove it on elliptic surfaces.

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