2020/04/20 by Armando Capasso, Capasso, Armando
Mathematics · #14D21 #14F05 #14J60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 14H60 #secondary 14D20
paper · pdf · doi:10.48550/arxiv.2004.09217
openalex publication_date 2020/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I consider Higgs bundles satisfying a notion of ampleness that was introduce Bruzzo, Graña Otero and Hernández Ruipérez, and prove that the Chern classes of rank r H-ample Higgs bundles over dimension n, polarized, smooth, complex, projective varieties are positive under opportune hypothesis. I extend this to non-negativeness of Chern classes of all numerically effective Higgs bundles; and use this condition to prove the vanishing of Chern classes of numerically flat Higgs bundles.