Parabolic Bogomolov--Gieseker Inequality and Pluriharmonic Metrics on Regular Parabolic Higgs Sheaves over Compact K\"ahler Manifolds

Tianshu Jiang; Jiayu Li

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arXiv · 2608.23787

Parabolic Bogomolov--Gieseker Inequality and Pluriharmonic Metrics on Regular Parabolic Higgs Sheaves over Compact K\"ahler Manifolds

Tianshu Jiang·Jiayu Li

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Abstract

We prove a parabolic Bogomolov--Gieseker inequality for stable regular parabolic Higgs sheaves on a compact K\"ahler manifold $(X,\omega)$ equipped with a simple normal crossing divisor $D$. We also prove that a polystable regular parabolic Higgs sheaf admits a pluriharmonic metric on $X\setminus D$, provided that each stable summand has parabolic degree zero and vanishing integrated second parabolic Chern character.

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Tianshu Jiang, Jiayu Li. 2026-08-24. Parabolic Bogomolov--Gieseker Inequality and Pluriharmonic Metrics on Regular Parabolic Higgs Sheaves over Compact K\"ahler Manifolds. https://arxiv.org/abs/2608.23787

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