Fourier-Mukai transform and index theory (Q1343710)

The authors consider relations between the Fourier-Mukai transform of a holomorphic vector bundle on a torus \(T\) of complex dimension two and the Nahm transform of the associated pair \((E, \nabla)\), where \(E\) is the \(C^\infty\) underlying bundle and \(\nabla\) is a compatible connection. After developing some general framework they give a global and simple proof of the equivalence between Mukai transform and Nahm transform of instantons and also a proof of Mukai's inversion theorem which circumvents the use of derived categories.