A weak compactness theorem of the Donaldson-Thomas instantons on compact Kähler threefolds

Abstract

In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by Higgs fields, and call Donaldson-Thomas equation, to analytically approach the Donaldson-Thomas invariants. In this article, we consider the equation on compact Kähler threefolds, and study some of analytic properties of solutions to them, using analytic methods in higher-dimensional Yang-Mills theory developed by Nakajima and Tian with some additional arguments concerning an extra non-linear term coming from the Higgs fields. We prove that a sequence of solutions to the Donaldson-Thomas equation of a unitary vector bundle over a compact Kähler threefold has a converging subsequence outside a closed subset whose real 2-dimensional Hausdorff measure is finite, provided that the L^2-norms of the Higgs fields are uniformly bounded. We also prove an n/2-compactness theorem of solutions to the equations on compact Kähler threefolds.

17 pages, final version, to appear in Journal of Mathematical Analysis and Applications

References in corpus (2)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• On the moduli space of Donaldson-Thomas instantons

Cited by in corpus (6)

• Deformations of nearly Kähler instantons
• A removal singularity theorem of the Donaldson-Thomas instantons on compact Kähler threefolds
• The behavior of sequences of solutions to the Hitchin-Simpson equations
• The DT-instanton equation on almost Hermitian 6-manifolds
• A stability of vector bundles with twisted sections and the Donaldson-Thomas instantons on compact Kähler threefolds
• The Donaldson-Thomas instantons on compact Kahler threefolds and a convergence