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Parabolic Bogomolov--Gieseker Inequality and Pluriharmonic Metrics on Regular Parabolic Higgs Sheaves over Compact Kähler Manifolds
Abstract
We prove a parabolic Bogomolov--Gieseker inequality for stable regular parabolic Higgs sheaves on a compact Kähler manifold (X,ω) equipped with a simple normal crossing divisor D. We also prove that a polystable regular parabolic Higgs sheaf admits a pluriharmonic metric on X∖ D, provided that each stable summand has parabolic degree zero and vanishing integrated second parabolic Chern character.
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BibTeX
@misc{jiang2026parabolic,
title = {{Parabolic Bogomolov--Gieseker Inequality and Pluriharmonic Metrics on Regular Parabolic Higgs Sheaves over Compact Kähler Manifolds}},
author = {Tianshu Jiang and Jiayu Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.23787},
eprint = {2608.23787},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.23787},
}
RIS
TY - UNPB
TI - Parabolic Bogomolov--Gieseker Inequality and Pluriharmonic Metrics on Regular Parabolic Higgs Sheaves over Compact Kähler Manifolds
AU - Tianshu Jiang
AU - Jiayu Li
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2608.23787
UR - https://arxiv.org/abs/2608.23787
AB - We prove a parabolic Bogomolov--Gieseker inequality for stable regular parabolic Higgs sheaves on a compact Kähler manifold (X,ω) equipped with a simple normal crossing divisor D. We also prove that a polystable regular parabolic Higgs sheaf admits a pluriharmonic metric on X∖ D, provided that each stable summand has parabolic degree zero and vanishing integrated second parabolic Chern character.
ER -