2002/04/30 by Francisco Santos · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #math.AG #math.CO #msc:52B11 #msc:52B20
paper · pdf · doi:10.1007/s00208-005-0643-5
published as Mathematische Annalen, 332:3 (2005), 645-665 · 18 pages, 2 figures. Except for Remark 2.6 (see below) changes w.r.t. version 2 are mostly minor editings suggested by an anonimous referee of "Mathematische Annalen". The paper has been accepted in that journal. Most of the contents of Remark 2.6 have been deleted, since there was a flaw in the argument
arxiv created 2003/11/13 · openalex publication_date 2005/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We construct small (50 and 26 points, respectively) point sets in dimension 5 whose graphs of triangulations are not connected. These examples improve our construction in J. Amer. Math. Soc., 13:3 (2000), 611--637 not only in size, but also in that their toric Hilbert schemes are not connected either, a question left open in that article. Additionally, the point sets can easily be put into convex position, providing examples of 5-dimensional polytopes with non-connected graph of triangulations.