D-Branes, Pi-Stability and Theta-Stability

Details D-Branes, Pi-Stability and Theta-Stability D-Branes, Pi-Stability and Theta-Stability

2004-07-14

arxiv.org/abs/hep-th/0407123v1

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, LaTeX, lecture given at "String Geometry", Snowbird 2004

Scientific paper

We investigate some aspects of Pi-stability of D-branes on Calabi-Yau threefolds in cases where there is a point in moduli space where the grades nearly or completely align. We prove that an example of complete alignment is the case of a collapsed del Pezzo surface. It is shown that there is an open neighbourhood of such a point for which Pi-stability reduces to theta-stability of quiver representations. This should be contrasted to the case of the large radius limit where mu-stability of sheaves cannot be extended out over an open neighbourhood.

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