  Considering the $D$-branes on a variety $Z$ as the objects of the derived
category $D^b(Z)$, we propose a definition for the charge of $D$-branes on not
necessarily smooth varieties. We define the charge $Q({\mathcal G})$ of
${\mathcal G}\in D^b(Z)$ as an element of the homology of $Z$, so that the
mapping $Q$ is compatible with the pushforward by proper maps between
varieties.
  Given a generic anticanonical hypersurface $Y$ of a toric variety $X$ defined
by a reflexive polytope, we express the charge of a line bundle on $Y$ defined
by a divisor $D$ of $X$ in terms of intersections of $D$ with cycles determined
by the polytope faces.
