numerically effective cotangent bundle; degree Frobenius splitting; Borel subgroup; parabolic subgroup; unipotent radical; flag variety; cotangent bundle; Koszul resolution; Borel-Bott-Weil theorem; Gorenstein singularity; rational singularity; Frobenius kernel; Dobeault vanishing; invariant form; characteristic \(p\); Steinberg module 