Non-connected toric Hilbert schemes

Details Non-connected toric Hilbert schemes Non-connected toric Hilbert schemes

2002-04-03

arxiv.org/abs/math/0204044v3

Mathematische Annalen, 332:3 (2005), 645-665

Mathematics

Combinatorics

18 pages, 2 figures. Except for Remark 2.6 (see below) changes w.r.t. version 2 are mostly minor editings suggested by an anon

Scientific paper

10.1007/s00208-005-0643-5

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.

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