Nilpotent Higgs bundles and the Hodge metric on the Calabi-Yau moduli

Abstract

We study an algebraic inequality for nilpotent matrices and show some interesting geometric applications: (i) obtaining topological information for nilpotent polystable Higgs bundles over a compact Riemann surface; (ii) obtaining a sharp upper bound of the holomorphic sectional curvatures of the period domain and the Hodge metric on the Calabi-Yau moduli.

27 pages, comments are welcome

Cited by in corpus (1)

• Domination results in $n$-Fuchsian fibers in the moduli space of Higgs bundles