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

TL;DR

This paper proves that certain singularities in solutions to the Donaldson-Thomas equation on compact K"ahler threefolds can be removed, extending understanding of the equation's analytic properties.

Contribution

It establishes a removal singularity theorem for Donaldson-Thomas instantons, showing that some singularities are removable on compact K"ahler threefolds.

Findings

Singularities in solutions can be removed under certain conditions.

Solutions converge smoothly outside a Hausdorff dimension two subset.

The result extends the analytic theory of Donaldson-Thomas equations.

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.