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

Masataka Iwai; Satoshi Jinnouchi; Shiyu Zhang

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

Algebraic Geometry 2026-07-21 v1 Complex Variables Differential Geometry

Authors: Masataka Iwai , Satoshi Jinnouchi , Shiyu Zhang

Abstract

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.

Keywords

orbifold Chern classes Fujiki class Miyaoka inequality nefness Bogomolov-Gieseker inequality

Cite

@article{arxiv.2607.18699,
  title  = {Semipositivity of the orbifold second Chern class in Fujiki's class},
  author = {Masataka Iwai and Satoshi Jinnouchi and Shiyu Zhang},
  journal= {arXiv preprint arXiv:2607.18699},
  year   = {2026}
}

Comments

v1: 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