Bogomolov Sheaf

A Bogomolov sheaf on a compact complex manifold is a holomorphic line bundle admitting a nonzero sheaf morphism with Iitaka dimension , for an integer . Here is the bundle of holomorphic -forms. In the compact Kähler setting, the absence of these sheaves characterizes specialness. For a compact Riemann surface of genus at least 2, the canonical bundle itself is a Bogomolov sheaf with . The definition involves section growth of the line bundle and a map into differential forms, rather than just the existence of a nonzero differential form.