Classification of semistable sheaves on a rational curve with one node

Abstract

We classify (semi)stable sheaves on a rational curve with one node. The results are based on the classification of indecomposable torsion-free sheaves due to Drozd and Greuel "Tame and wild projective curves and classification of vector bundles", where the sheaves are described in terms of certain combinatorial data. We translate the condition of (semi)stability into this combinatorial language and solve the so obtained problem.