Communications in Number Theory and Physics
Volume 4 (2010)
On a computation of rank two Donaldson–Thomas invariants
Pages: 49 – 102
For a Calabi–Yau three-fold $X$, we explicitly compute theDonaldson–Thomas-type invariant counting pairs $(F, V)$,where $F$ is a zero-dimensional coherent sheaf on $X$ and$V\subset F$ is a two-dimensional linear subspace, whichsatisfy a certain stability condition. This is a rank twoversion of the Donaldson–Thomas (DT)-invariant of rankone, studied by Li, Behrend-Fantechi andLevine-Pandharipande. We use the wall-crossing formula ofDT-invariants established by Joyce-Song,Kontsevich-Soibelman.