Virtual Poincare polynomial of moduli space of semistable sheaves of rank two on reducible curves

Abstract

The main purpose of this paper is to give an explicit description of the moduli space of semistable sheaves of rank two on a stable curve C obtained by gluing two smooth curves at a point. We prove that the moduli space is irreducible and birational to a projective bundle over the moduli space of stable vector bundles on each component curve, independently of the choice of polarization. As an application, we compute the virtual Poincare polynomial of the moduli space.