Abstract
We prove that the combinatorial types of those cone systems which correspond to complete smooth toric varieties are more restricted than for complete toric varieties: the toric varieties corresponding to essentially all types of cyclic polytopes possess singularities. This yields a negative answer to a problem stated by G. Ewald. Some consequences and problems concerning mathematical programming and the rational cohomology of smooth toric varieties are discussed.
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The research of P. Kleinschmidt was supported in part by the Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, Minnesota, USA.
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Gretenkort, J., Kleinschmidt, P. & Sturmfels, B. On the existence of certain smooth toric varieties. Discrete Comput Geom 5, 255–262 (1990). https://doi.org/10.1007/BF02187789
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DOI: https://doi.org/10.1007/BF02187789