On a computation of rank two Donaldson-Thomas invariants

Abstract

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.

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

References in corpus (4)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Donaldson-Thomas invariants via microlocal geometry
• Zero dimensional Donaldson-Thomas invariants of threefolds
• Curve counting theories via stable objects I. DT/PT correspondence

Cited by in corpus (9)

• Wall-Crossing from Boltzmann Black Hole Halos
• Wall Crossing, Quivers and Crystals
• Rank Two ADHM Invariants and Wallcrossing
• Wallcrossing and Cohomology of The Moduli Space of Hitchin Pairs
• On higher rank Donaldson-Thomas invariants
• Donaldson-Thomas invariants of certain Calabi-Yau 3-folds
• D0-D6 states counting and GW invariants
• Weighted Euler characteristic of the moduli space of higher rank Joyce-Song pairs
• M theory and the Coulomb phase of higher rank DT invariants