A point set whose space of triangulations is disconnected
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- by Francisco Santos
- J. Amer. Math. Soc. 13 (2000), 611-637
- DOI: https://doi.org/10.1090/S0894-0347-00-00330-1
- Published electronically: March 29, 2000
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Abstract:
By the “space of triangulations" of a finite point configuration $\mathcal {A}$ we mean either of the following two objects: the graph of triangulations of $\mathcal {A}$, whose vertices are the triangulations of $\mathcal {A}$ and whose edges are the geometric bistellar operations between them or the partially ordered set (poset) of all polyhedral subdivisions of $\mathcal {A}$ ordered by coherent refinement. The latter is a modification of the more usual Baues poset of $\mathcal {A}$. It is explicitly introduced here for the first time and is of special interest in the theory of toric varieties. We construct an integer point configuration in dimension 6 and a triangulation of it which admits no geometric bistellar operations. This triangulation is an isolated point in both the graph and the poset, which proves for the first time that these two objects cannot be connected.References
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Bibliographic Information
- Francisco Santos
- Affiliation: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, E-39005, Santander, Spain
- MR Author ID: 360182
- ORCID: 0000-0003-2120-9068
- Email: santos@matesco.unican.es
- Received by editor(s): August 3, 1999
- Received by editor(s) in revised form: March 6, 2000
- Published electronically: March 29, 2000
- Additional Notes: This research was partially supported by grant PB97–0358 of the Spanish Dirección General de Enseñanza Superior e Investigación Científica.
- © Copyright 2000 American Mathematical Society
- Journal: J. Amer. Math. Soc. 13 (2000), 611-637
- MSC (2000): Primary 52B11; Secondary 52B20
- DOI: https://doi.org/10.1090/S0894-0347-00-00330-1
- MathSciNet review: 1758756