Vanishing Chern classes for numerically flat Higgs bundles

Research paper by Armando Capasso

Indexed on: 21 Apr '20Published on: 20 Apr '20Published in: arXiv - Mathematics - Algebraic Geometry


I consider Higgs bundles satisfying a notion of ampleness that was introduce Bruzzo, Gra\~na Otero and Hern\'andez Ruip\'erez, 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.