Sheaves with canonical determinant on Cohen–Macaulay schemes

This paper studies the class of sheaves which lie on arithmetically Cohen–Macaulay schemes and which have as determinant a twist of the canonical sheaf. Special emphasis is placed on finding minimal, sufficient cohomological conditions which ensure that the top dimensional component of regular sections of the dual of these sheaves vanish along arithmetically Gorenstein schemes. Duals of odd rank Buchsbaum–Rim sheaves, normal sheaves to licci schemes, certain sheafified Koszul homology modules and various other families are shown to satisfy the requisite conditions.