D-Branes, Pi-Stability and Theta-Stability
Abstract
Description
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.
16 pages, LaTeX, lecture given at "String Geometry", Snowbird 2004
16 pages, LaTeX, lecture given at "String Geometry", Snowbird 2004