On the moduli space of Donaldson-Thomas instantons

Abstract

In alignment with a programme by Donaldson and Thomas [DT], Thomas [Th] constructed a deformation invariant for smooth projective Calabi-Yau threefolds, which is now called the Donaldson-Thomas invariant, from the moduli space of (semi-)stable sheaves by using algebraic geometry techniques. In the same paper [Th], Thomas noted that certain perturbed Hermitian-Einstein equations might possibly produce an analytic theory of the invariant. This article sets up the equations on symplectic 6-manifolds, and gives the local model and structures of the moduli space coming from the equations. We then describe a Hitchin-Kobayashi style correspondence for the equations on compact Kähler threefolds, which turns out to be a special case of results by Alvarez-Consul and Garcia-Prada [AG].

20 pages, final version, to appear in Extracta Mathematicae

Cited by in corpus (6)

• On orientations for gauge-theoretic moduli spaces
• Conjectures on counting associative 3-folds in $G_2$-manifolds
• A weak compactness theorem of the Donaldson-Thomas instantons on compact Kähler threefolds
• Stable sheaves with twisted sections and the Vafa-Witten equations on smooth projective surfaces
• 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