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JCT

2007

2007

We show that the Ehrhart h-vector of an integer Gorenstein polytope with a unimodular triangulation satisﬁes McMullen’s g-theorem; in particular it is unimodal. This result generalizes a recent theorem of Athanasiadis (conjectured by Stanley) for compressed polytopes. It is derived from a more general theorem on Gorenstein afﬁne normal monoids M: one can factor K[M] (K a ﬁeld) by a “long” regular sequence in such a way that the quotient is still a normal afﬁne monoid algebra. In the case of a polytopal Gorenstein normal monoid E(P), this technique reduces all questions about the Ehrhart h-vector to a normal Gorenstein polytope Q with exactly one interior lattice point. (These are the normal ones among the reﬂexive polytopes considered in connection with mirror symmetry.) If P has a unimodular triangulation, then it follows readily that the Ehrhart hvector of P coincides with the h-vector of the boundary complex of a simplicial polytope, and the g-theorem applies.

Added |
15 Dec 2010 |

Updated |
15 Dec 2010 |

Type |
Journal |

Year |
2007 |

Where |
JCT |

Authors |
Winfried Bruns, Tim Römer |

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