D-Branes on Toric Calabi-Yau Varieties

Details D-Branes on Toric Calabi-Yau Varieties D-Branes on Toric Calabi-Yau Varieties

2008-06-16

arxiv.org/abs/0806.2612v2

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, counterexample to global tilting set added, refs added, conventions made more sane

Scientific paper

We analyze B-type D-branes on noncompact toric Calabi--Yau spaces. A general program is presented to find a set of tilting line bundles that yields the associated quiver and its relations. In many cases, this set remains fixed as one moves between phases in the K\"ahler moduli space. This gives a particularly simple picture of how the derived category remains invariant across all phases. The combinatorial problems involving local cohomology used to determine the tilting set are also related to questions of Pi-stability as one moves between phases. As a result, in some cases precisely those line bundles in the tilting set remain stable over the whole moduli space in some sense.

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