On a computation of rank two Donaldson-Thomas invariants

Details On a computation of rank two Donaldson-Thomas invariants On a computation of rank two Donaldson-Thomas invariants

2009-12-13

arxiv.org/abs/0912.2507v2

Mathematics

Algebraic Geometry

The computation of \Omega(2, 3) was wrong in the first version, and I have corrected it

Scientific paper

For a Calabi-Yau 3-fold $X$, we explicitly compute the Donaldson-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, which satisfy a certain stability condition. This is a rank two version of the DT-invariant of rank one, studied by Li, Behrend-Fantechi and Levine-Pandharipande. We use the wall-crossing formula of DT-invariants established by Joyce-Song, Kontsevich-Soibelman.

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