  This paper describes how, in the case of algebraic surfaces, the well-known
theorem of Donaldson-Uhlenbeck-Yau can be proved in a framework of generalized
'multiplier ideal sheaves', following the ideas of Siu. The key concept is that
the destabilizing sheaf satisfies a differential inclusion relation. This
relation is used, together with a complex Frobenius theorem for locally
finitely generated subsheaves, to imply coherence of the destabilizing
subsheaf.
