A Weak Compactness Theorem of the Donaldson-thomas Instantons on Compact Kähler Threefolds, I

We call these equations the Donaldson-Thomas equations, and a solution (A,u) to these equations Donaldson-Thomas instanton. In [Ta1], we studied local structures of the moduli space of the DonaldsonThomas instantons such as the infinitesimal deformation and the Kuranishi map of the moduli space. In this article, we prove a weak compactness theorem of the Donaldson-Thomas instantons. This describes bubbling phenomena of the Donaldson-Thomas instantons at the initial phase.