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D-Branes, Pi-Stability and Theta-Stability

Paul S. Aspinwall
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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.

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Paul S. Aspinwall. 2004-07-14. D-Branes, Pi-Stability and Theta-Stability. https://arxiv.org/abs/hep-th/0407123

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