Subdivisions of toric complexes

Autor(en): Brun, M
Romer, T 
Stichwörter: CONFIGURATIONS; edgewise subdivision; face ring; initial ideal; INITIAL IDEALS; Mathematics; polyhedral complex; regular subdivision; toric ideal
Erscheinungsdatum: 2005
Herausgeber: SPRINGER
Journal: JOURNAL OF ALGEBRAIC COMBINATORICS
Volumen: 21
Ausgabe: 4
Startseite: 423
Seitenende: 448
Zusammenfassung: 
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.
ISSN: 09259899
DOI: 10.1007/s10801-005-3020-2

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