A logarithmic Bogomolov--Sommese vanishing theorem on compact Kähler manifolds

In this paper, we establish a logarithmic Bogomolov–Sommese vanishing theorem in terms of numerical dimension for pseudo-effective line bundles on compact Kähler manifolds. As an application, we obtain a rigidity result with vanishing second Chern class for logarithmic cotangent bundles by combining the vanishing theorem with a structure theorem of Iwai and Matsumura.