Communications in Number Theory and Physics

Volume 4 (2010)

Number 1

On a computation of rank two Donaldson–Thomas invariants

Pages: 49 – 102



Yukinobu Toda (Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo, Kashiwa, Japan)


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.

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