AI 中文总结
研究藤木类中紧致正规解析簇orbifold第二陈类不等式，通过建立切层和余切层一般nef性定理及相关不等式，证明宫冈不等式及orbifold第二陈类半正性。
AI 中文摘要
我们研究了藤木类中紧致正规解析簇的orbifold第二陈类的不等式。我们证明了藤木类中具有nef典范除子的奇异簇的宫冈不等式，以及具有nef反典范除子的簇的orbifold第二陈类的半正性。为证明这些结果，我们建立了切层和余切层的一般nef性定理以及混合极化的orbifold博戈莫洛夫 - 吉塞克不等式。
英文摘要
We study inequalities for orbifold second Chern classes of compact normal analytic varieties in Fujiki's class. We prove Miyaoka's inequality for singular varieties in Fujiki's class with nef canonical divisor, as well as the semipositivity of the orbifold second Chern class for varieties with nef anti-canonical divisor. To prove these results, we establish generic nefness theorems for tangent and cotangent sheaves and an orbifold Bogomolov--Gieseker inequality for mixed polarizations.
Commentsv1: 26 pages; An earlier version of this paper was included as the second part of arXiv:2507.08522. The original manuscript has since been divided into two independent papers. Comments are welcome
