zbMATH — the first resource for mathematics

Rank 2 reflexive sheaves on a smooth threefold. (English) Zbl 1183.14026
Summary: We show that some properties of rank 2 reflexive sheaves true on \(\mathbb{P}^3\) can be extended to a wide class of smooth projective threefolds, including smooth 3-dimensional complete intersections and some Fano threefolds. In particular, we extend the Hartshorne-Serre correspondence between rank 2 reflexive sheaves and curves lying on the threefold. Also, we establish the non-negativity of the third Chern class of a rank 2 reflexive sheaf.

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14J30 \(3\)-folds
Full Text: Link