Symplectic structures on moduli spaces of framed sheaves on surfaces

After a brief introduction on the theory of framed sheaves
and their moduli spaces, I will give a description of a modified Atiyah class of a family of framed sheaves, which allows to define a framed version of the Kodaira-Spencer map. Moreover, I will construct closed two-forms on the moduli spaces of framed sheaves on surfaces.
As an application, I will define a symplectic structure on the moduli spaces of framed sheaves on the second Hirzebruch surface. This generalizes a result of Bottacin for the locally free case.