Torsion free sheaves over a nodal curve of arithmetic genus one

Abstract

We classify all isomorphism classes of stable torsionfree sheaves on an irreducible nodal curve of arithmetic genus one defined over C. Let X be a nodal curve of arithmetic genus one defined over R, with exactly one node, such that X does not have any real points apart from the node. We classify all isomorphism classes of stable real algebraic torsion free sheaves over X of even rank. We also classify all isomorphism classes of real algebraic torsion free sheaves over X of rank one.