Coherent Sheaves on Singular Projective Curves with Nodal Singularities

2001/01/17 by I. Burban, Burban, I., Yu. Drozd +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.math/0101140

21 page, 17 figures

arxiv created 2001/01/17 · arxiv updated 2009/11/30

Abstract

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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