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

Abstract

Let Y be a smooth Calabi–Yau hypersurface of P 1 × P where P 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 ¯ 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.