A removal singularity theorem of the Donaldson-Thomas instantons on compact K\"ahler threefolds

Abstract

We consider a perturbed Hermitian-Einstein equation, which we call the Donaldson-Thomas equation, on compact K\"ahler threefolds. In arXiv:0805.2195, we analysed some analytic properties of solutions to the equation, in particular, we proved that a sequence of solutions to the Donaldson-Thomas equation has a subsequence which smoothly converges to a solution to the Donaldson-Thomas equation outside a closed subset of the Hausdorff dimension two. In this article, we prove that some of these singularities can be removed.