Degenerations of Instantons

Abstract

We consider in this lecture the degenerations of “physical instantons” as algebraic vector bundles on ℙ₃(ℂ). These are the vector bundles which correspond to self-dual SU(2)— Yang-Mills potentials on the 4-sphere by the Atiyah-Ward correspondence [l]. In 2. we characterise most of the sheaves in ℙ₃(ℂ) which are degenerations of instantons. In 3. we give an algebraic construction of the Donaldson compactification of I(n), and in 4. we interprete the degenerations as global equivalence classes of singular connections in the generic case, thereby obtaining a precise algebraic description of bubbling out of instantons. Details can be found in [3] and [4].