2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101223We compute the expected dimension of the moduli space of torsion-free rank 2 sheaves at a point corresponding to a stable reflexive sheaf and give conditions for the existence of a perfect tangent-obstruction complex on a class of smooth projective threefolds; this class includes Fano and Calabi-Yau threefolds. We also explore both local and global relationships between moduli spaces of reflexive rank 2 sheaves and the Hilbert scheme of curves.17 pages. Entire paper rewritten - discusses relationship between moduli spaces of reflexive rank 2 sheaves and the Hilbert scheme of curves; brief mention of Donaldson-Thomas invariantsAlgebraic Geometry14F05, 14D20, 14J60text