An explicit lattice point realization is provided for the primary<br>
components of an arbitrary binomial ideal in characteristic zero.<br>
This decomposition is derived from a characteristic-free<br>
combinatorial description of certain primary components of<br>
binomial ideals in affine semigroup rings, namely those that are<br>
associated to faces of the semigroup.  These results are<br>
intimately connected to hypergeometric differential equations in<br>
several variables.