The paper proves a Bogomolov-Gieseker type inequality for local P^3 and uses it to construct families of geometric stability conditions and boundary points of the geometric chamber.
Dirichlet branes, homological mirror symmetry, and stability
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abstract
We discuss some mathematical conjectures which have come out of the Dirichlet branes in superstring theory, focusing on the case of supersymmetric branes in Calabi-Yau compactification. This has led to the formulation of a notion of stability for objects in a derived category, contact with Kontsevich's homological mirror symmetry conjecture, and "physics proofs" for many of the subsequent conjectures based on it, such as the representation of Calabi-Yau monodromy by autoequivalences of the derived category.
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Stability conditions on the canonical line bundle of $\mathbb{P}^3$
The paper proves a Bogomolov-Gieseker type inequality for local P^3 and uses it to construct families of geometric stability conditions and boundary points of the geometric chamber.