On the moduli space of Donaldson-Thomas instantons

Yuuji Tanaka

Published 2008-05-15, updated 2015-02-17Version 4

In alignment with a programme by Donaldson and Thomas, Thomas 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, Thomas noted that a perturbed Hermitian-Einstein equation might possibly produce an analytic theory of the invariant. This article sets up the equation on symplectic 6-manifolds, describes the local model and structures of the moduli space coming from the equation by familiar techniques in gauge theory, and also mentions a Hitchin-Kobayashi style correspondence for the equation on compact Kaehler threefolds.