Geodesic
Subdivisions of toric complexes
Journal of Algebraic Combinatorics, Tome 21 (2005) no. 4, pp. 423-448.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 extends Stanley and Reisner's face ring for abstract simplicial complexes [20] and Stanley's face ring for rational fans [21]. 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 in [23]. We apply our results to study edgewise subdivisions of abstract simplicial complexes.
Keywords: keywords initial ideal, toric ideal, polyhedral complex, regular subdivision, edgewise subdivision, face ring 
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     title = {Subdivisions of toric complexes},
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Brun, Morten; Römer, Tim. Subdivisions of toric complexes. Journal of Algebraic Combinatorics, Tome 21 (2005) no. 4, pp. 423-448. http://geodesic.mathdoc.fr/item/JAC_2005__21_4_a1/