Coherent Sheaves on Singular Projective Curves with Nodal Singularities

Details Coherent Sheaves on Singular Projective Curves with Nodal Singularities Coherent Sheaves on Singular Projective Curves with Nodal Singularities

2001-01-17

arxiv.org/abs/math/0101140v1

Mathematics

Algebraic Geometry

21 page, 17 figures

Scientific paper

We give the full answer to the question: on which curves the category of coherent sheaves $\Coh_{X}$ is tame. The answer is: these are just the curves from the list of Drozd-Greuel. Moreover, in this case the derived category $D^{-}(\Coh_{X})$ is also tame. We give an explicit description of the objects of this category as well as of the categories $D^{b}(\Coh_{X})$, $\Coh_{X}$. Among the coherent sheaves we describe the vector bundles, torsion-free sheaves, mixed sheaves and skyscraper sheaves.

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