  Various topological properties of D-branes in the type--IIA theory are
captured by the topologically twisted B-model, treating D-branes as objects in
the bounded derived category of coherent sheaves on the compact part of the
target space. The set of basic D-branes wrapped on the homology cycles of the
compact space are taken to reside in the heart of t-structures of the derived
category of coherent sheaves on the space at any point in the K\"ahler moduli
space. The stability data entails specifying a t-structure along with a grade
for sorting the branes. Considering an example of a degenerate Calabi-Yau
space, obtained via geometric engineering, that retains but a projective curve
as the sole non-compact part, we identify the regions in the K\"ahler moduli
space of the curve that pertain to the different t-structures of the bounded
derived category of coherent sheaves on the curve corresponding to the
different phases of the topological branes.
