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 Wall-crossing and invariants of higher rank stable pairs


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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.



Author: Artan Sheshmani

Source: https://archive.org/



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