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Non-connected toric Hilbert schemes

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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 the associated 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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  1. Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, E-39005, Santander, Spain

    Francisco Santos

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  1. Francisco Santos
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Correspondence to Francisco Santos.

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Mathematics Subject Classification (2000): Primary 52B11; Secondary 52B20

The main result in this paper was obtained in the fall of 2001, while I was a visiting professor in the Department of Mathematics, U.C. Davis, supported by U. C. Davis, M.S.R.I. and the Spanish Government. I am also partially supported by grant BFM2001–1153 of the Spanish Dirección General de Enseñanza Superior e Investigación Científica. The paper is dedicated to Bernd Sturmfels on his 40th birthday.

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Santos, F. Non-connected toric Hilbert schemes. Math. Ann. 332, 645–665 (2005). https://doi.org/10.1007/s00208-005-0643-5

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