We study the derived categories of coherent sheaves on some singular projective curves and give a complete description of indecomposable objects using the technique of matrix problems.
"Coherent sheaves on rational curves with simple double points and transversal intersections." Duke Math. J. 121 (2) 189 - 229, 1 February 2004. https://doi.org/10.1215/S0012-7094-04-12121-9