抄録
In this paper we answer a question posed by Batyrev, which asks if there exists a complete regular fan with more than quadratically many primitive collections. We construct a smooth projective toric variety associated to a complete regular d-dimensional fan with n generators where the number of primitive collections is at least exponential in n-d. We also exhibit the connection between the number of primitive collections and the facet complexity of the Gröbner fan of the associated integer program.
