  In these notes we review recent work on describing D-branes with nonzero
Higgs vevs in terms of sheaves, which gives a physical on-shell D-brane
interpretation to more sheaves than previously understood as describing
D-branes. The mathematical ansatz for this encoding is checked by comparing
open string spectra between D-branes with nonzero Higgs vevs to Ext groups
between the corresponding sheaves. We illustrate the general methods with a few
examples.
