Abundance theorem for minimal compact Kähler manifolds with vanishing second Chern class

Abstract: In this paper, for compact K\"ahler manifolds with nef cotangent bundle, we study the abundance conjecture and the associated Iitaka fibrations. We show that, for a minimal compact K\"ahler manifold, the second Chern class vanishes if and only if the cotangent bundle is nef and the canonical bundle has the numerical dimension $0$ or $1$. Additionally, in this case, we prove that the canonical bundle is semi-ample. Furthermore, we give a relation between the variation of the fibers of the Iitaka fibration and a certain semipositivity of the cotangent bundle.