Aspinwall, PS; Lawrence, A, *Derived categories and zero-brane stability*,
Journal of High Energy Physics, vol. 5 no. 8
(2001),
pp. XIV-26 .
**Abstract:**

*We define a particular class of topological field theories associated to open strings and prove the resulting D-branes and open strings form the bounded derived category of coherent sheaves. This derivation is a variant of some ideas proposed recently by Douglas. We then argue that any 0-brane on any Calabi-Yau threefold must become unstable along some path in the Kähler moduli space. As a byproduct of this analysis we see how the derived category can be invariant under a birational transformation between Calabi-Yaus.*