We provide generalizations of the notions of Atiyah class and Kodaira-Spencer
map to the case of framed sheaves. Moreover, we construct closed two-forms on
the moduli spaces of framed sheaves on surfaces. As an application, we define a
symplectic structure on the moduli spaces of framed sheaves on some
birationally ruled surfaces.Comment: v2: final version to appear in Centr. Eur. J. Math, section
"Examples" improved: we obtain new examples of non-compact holomorphic
symplectic varietie
