A point set whose space of triangulations is disconnected
By the ``space of triangulations" of a finite point configuration we mean either of the following two objects: the graph of triangulations of , whose vertices are the triangulations of and whose edges are the geometric bistellar operations between them or the partially ordered set (poset) of al...
| Autor: | |
|---|---|
| Tipo de documento: | artigo |
| Data de publicação: | 2000 |
| País: | España |
| Recursos: | Universidad de Cantabria (UC) |
| Repositório: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.unican.es:10902/2584 |
| Acesso em linha: | http://hdl.handle.net/10902/2584 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Triangulation Point configuration Bistellar flip Polyhedral subdivision Baues problem |
| Resumo: | By the ``space of triangulations" of a finite point configuration we mean either of the following two objects: the graph of triangulations of , whose vertices are the triangulations of and whose edges are the geometric bistellar operations between them or the partially ordered set (poset) of all polyhedral subdivisions of ordered by coherent refinement. The latter is a modification of the more usual Baues poset of . 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. |
|---|