Unimodular triangulations of multiples of 3-polytopes

Francisco Santos
University of Cantabria

A seminal result in the theory of toric varieties, due to Knudsen and Mumford (1973) asserts that for every lattice polytope $P$ there is a positive integer $k$ such that the dilated polytope $kP$ has a unimodular triangulation. In dimension 3, Kantor and Sarkaria (2003) have shown that $k=4$ works for every polytope. But this does not imply that every $k\ge 4$ works as well. In this talk I show that every $k\ge 4$ works, except perhaps for $k \in \{5,7,11\}$. This follows from the following two lemmas: (a) Every composite $k$ works. (b) The values of $k$ that work form a semigroup.

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