Nilpotent Higgs Bundles and the Hodge Metric on the Calabi–Yau Moduli

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.

Hyperbolicity of Varieties Supporting a Variation of Hodge Structure

We generalize former results of Zuo and the 1st author showing some hyperbolicity properties of varieties supporting a variation of Hodge structure. Our proof only uses the special curvature properties of period domains. In particular, in contrast to the former approaches, it does not use any result on the asymptotic behavior of the Hodge metric.