Uhlenbeck compactification as a functor

We give a definition of a functor compactifying the functor of bundles on a surfaces. Earlier different authors have defined similar spaces as either images under a morphism or a quotient by an equivalence relation. We use the technique of multiplicative functors to explain what kind of objects are parameterized by the points of this compactification.Comment: to appear in IMR

Moduli of Sheaves on Surfaces and Action of the Oscillator Algebra

Let S be a smooth projective algebraic surface. Generalizing results of Nakajima and Grojnowski, we construct (under some assumptions) an action of the oscillator algebra associated to the cohomology of S, on the cohomology of the moduli spaces of stable rank r sheaves on S.Comment: 35 pages, Latex2e, some typos and references correcte