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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.

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