Derived categories of nodal curves

Abstract

A playing an important role in the theory of vector bundles over projective curves and in the theory of Cohen‐Macaulay modules [2, 3]. It is also proved that, with the exception of these curves and certain weighted projective Geigle‐Lenzing straight lines [4], all other noncommutative curves are wild relative to the classification of vector bundles. In the present paper, we prove that, for nodal curves of string and almost string types, it is possible to describe not only vector bundles but also the derived categories of coherent sheaves in complete agreement with the fact that this description is possible for linear configurations of the types A and Q