Wall-crossing and invariants of higher rank stable pairs

Wall-crossing and invariants of higher rank stable pairs

Tue, 18/01/2011
15:45 		Artan Sheshmani (University of Illinois at Urbana Champaign) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Wall-crossing and invariants of higher rank stable pairs
We introduce a higher rank analog of Pandharipande-Thomas theory of stable pairs. Given a Calabi-Yau threefold $ X $, we define the higherrank 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.