D-Branes, Pi-Stability and Theta-Stability

Abstract

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

References in corpus (6)

• The spectrum of BPS branes on a noncompact Calabi-Yau
• Fractional Branes and Boundary States in Orbifold Theories
• Toric Duality Is Seiberg Duality
• D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds
• D-Brane Stability and Monodromy
• Dibaryons from Exceptional Collections

Cited by in corpus (9)

• Stability of Landau-Ginzburg branes
• Moduli Spaces for D-branes at the Tip of a Cone
• Geometry of Particle Physics
• Lectures on D-branes, Gauge Theories and Calabi-Yau Singularities
• Stability Conditions and Branes at Singularities
• Parameter Space of Quiver Gauge Theories
• Probing Geometry with Stability Conditions
• Exponential Networks for Linear Partitions
• Wall-crossing, Toric divisor and Seiberg duality