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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.

preprint2020arXivOpen access
Qiongling Li
math.AGmath.DG
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Qiongling Li

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