We show that some properties of rank 2 reflexive sheaves true on P^3 can be extended to a wide class of smooth pro jective 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 ot the third Chern class of a rank 2 reflexive sheaf.
Rank 2 reflexive sheaves on a smooth threefold
VALENZANO, Mario
2004-01-01
Abstract
We show that some properties of rank 2 reflexive sheaves true on P^3 can be extended to a wide class of smooth pro jective 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 ot the third Chern class of a rank 2 reflexive sheaf.
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