Seminar series
Date
Tue, 18 Jan 2011
Time
15:45 -
16:45
Location
L3
Speaker
Artan Sheshmani
Organisation
University of Illinois at Urbana Champaign
We introduce a higher rank analog of Pandharipande-Thomas theory of stable pairs. Given a Calabi-Yau threefold $X$, we define the higher
rank stable pairs (which we call frozen triples) given by the data $(F,\phi)$ where $F$ is a pure coherent sheaf with one dimensional support over $X$ and $\phi:{\mathcal O}^r\rightarrow F$ is a map. We compute the Donaldson-Thomas type invariants associated to the 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 a higher rank enumerative theory of stable pairs over a Calabi-Yau threefold, and we computed similar invariants using Graber-Pandharipande virtual localization technique.
rank stable pairs (which we call frozen triples) given by the data $(F,\phi)$ where $F$ is a pure coherent sheaf with one dimensional support over $X$ and $\phi:{\mathcal O}^r\rightarrow F$ is a map. We compute the Donaldson-Thomas type invariants associated to the 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 a higher rank enumerative theory of stable pairs over a Calabi-Yau threefold, and we computed similar invariants using Graber-Pandharipande virtual localization technique.