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.

中文翻译：

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幂零希格斯束和卡拉比-丘模量的霍奇度量

我们研究了幂零矩阵的代数不等式并展示了一些有趣的几何应用：（i）在紧黎曼曲面上获得幂零多稳态希格斯束的拓扑信息；(ii) 获得周期域的全纯截面曲率和卡拉比-丘模量的霍奇度量的尖锐上限。