Moduli spaces of stable bundles on Calabi-Yau varieties and Donaldson-Thomas invariants

Let Y be a smooth Calabi-Yau hypersurface of P(1) x P where IF stands for a P(d)-bundle over P(1). We will prove that for many ample line bundles L and certain Chern characters c, the moduli space (M) over bar (L)(c) (resp.M(L)(c)) of L-Gieseker semistable (resp. L-stable) rank two torsion free sheaves (resp. vector bundles) on Y with Chern character c are smooth and irreducible and we will compute its dimension. Moreover, we will prove that both moduli spaces coincide. As a byproduct of the geometrical description of these moduli spaces, we will compute the Donaldson-Thomas invariants of some Calabi-Yau 3-folds. (C) 2011 Elsevier B.V. All rights reserved.