AI 中文总结
该研究针对配备简单正常交叉除子的紧Kähler流形，证明了稳定正则抛物Higgs层的抛物Bogomolov–Gieseker不等式，并给出多稳定正则抛物Higgs层在去奇点集上存在多重调和度量的条件。
AI 中文摘要
我们对配备简单正常交叉除子D的紧Kähler流形(X,ω)上的稳定正则抛物Higgs层，证明了抛物Bogomolov–Gieseker不等式。我们还证明，若每个稳定直和项的抛物次数为零且积分后的二阶抛物陈特征为零，则多稳定正则抛物Higgs层在X\D上容许多重调和度量。
英文摘要
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 \(X\setminus D\), provided that each stable summand has parabolic degree zero and vanishing integrated second parabolic Chern character.
Comments108 pages; revised and reorganized
