The Spectrum of $BPS$ Branes on a Noncompact Calabi-Yau

We begin the study of the spectrum of BPS branes and its variation on lines of marginal stability on 2(?3), a Calabi-Yau ALE space asymptotic to 3/3. We show how to get the complete spectrum near the large volume limit and near the orbifold point, and find a striking similarity between the descriptions of holomorphic bundles and BPS branes in these two limits. We use these results to develop a general picture of the spectrum. We also suggest a generalization of some of the ideas to the quintic Calabi-Yau.