  We introduce toric complexes as polyhedral complexes consisting of rational
cones together with a set of integral generators for each cone, and we define
their associated face rings. Abstract simplicial complexes and rational fans
can be considered as toric complexes, and the face ring for toric complexes
extend Stanley and Reisner's face ring for abstract simplicial complexes and
Stanley's face ring for rational fans. Given a toric complex with defining
ideal I for the face ring we give a geometrical interpretation of the initial
ideals of I with respect to weight orders in terms of subdivisions of the toric
complex generalizing a theorem of Sturmfels. We apply our results to study
edgewise subdivisions of abstract simplicial complexes.
