numerically effective cotangent bundle; degree compact Kähler manifold; Kähler manifold; nef line bundle; positive vector bundle; numerically effective line bundle; positive holomorphic vector bundle; multiplier ideal sheaf; almost plurisubharmonic function; big line bundle; vanishing theorems; numerical Kodaira dimension; hermitian metric on vector bundles; Hodge star operator; Kähler metric; coherent analytic sheaf 