Semipositivity of the orbifold second Chern class in Fujiki's class

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.