Mathematics – Algebraic Geometry
Scientific paper
2011-01-12
Mathematics
Algebraic Geometry
Revised version, 42 pages
Scientific paper
We introduce a higher rank analogue of the Pandharipande-Thomas theory of stable pairs. Given a Calabi-Yau threefold $X$, we define the frozen triples given by the tuple $(E,F,\phi)$ in which $E$ is a coherent sheaf isomorphic to $O(-n)^r$, $F$ is a pure coherent sheaf with one dimensional support and $\phi$ is given by a morphism from $E$ to $F$. In this article we compute the Donaldson-Thomas type invariants associated to frozen triples using the wall-crossing formula of Joyce-Song and Kontsevich-Soibelman. This work is a sequel to arxiv.1011.6342 where we gave a deformation theoretic construction of an enumerative theory of higher rank stable pairs and using the virtual localization technique computed similar invariants over a Calabi-Yau threefold.
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