Smoothable varieties with torsion free canonical sheaf (Q1824663)

Let X be a d-dimensional smoothable Cohen-Macaulay projective variety. Consider the canonical map \(c:\quad \Omega^ d_ X\to \omega_ X.\) Let L be an ample line bundle on X. By a clever calculation involving \(\chi (\Omega^ d_ X\otimes L^ N)\) for \(N\gg 0\), the author shows that if c is injective, then c is an isomorphism and X is smooth by a theorem of Kunz and Waldi.