Stable reflexive sheaves on smooth projective 3-folds (Q816319)

The paper finds new upper bounds for the third Chern class of a rank two reflexive sheaf on a smooth projective threefold, with a clear and explicit computation in the case of a smooth hypersurface in \(\mathbb{P}^4\) of degree \(d > 2\). It also finds bounds for the vanishing of higher cohomology and the existence of non-zero global sections. The paper is based on \textit{R. Hartshorne}'s theory of reflexive sheaves on \(\mathbb{P}^3\) (that can easily be extended to a smooth threefold [see Math. Ann. 238, 229--280 (1978; Zbl 0411.14002); ibid. 254, 121--176 (1980; Zbl 0431.14004); see also \textit{M. Valenzano}, Rend. Semin. Mat., Torino 62, 235--254 (2004; Zbl 1183.14026)]).