On the Complexity of Smooth Projective Toric Varieties
Abstract
In this paper we answer a question posed by V.V. Batyrev. The question asked 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 fan $\Delta$ in R^d with $n$ generators where the number of primitive collections of $\Delta$ is at least exponential in $nd$. We also exhibit the connection between the number of primitive collections of $\Delta$ and the facet complexity of the Gröbner fan of the associated integer program.
 Publication:

arXiv eprints
 Pub Date:
 November 1996
 arXiv:
 arXiv:alggeom/9611010
 Bibcode:
 1996alg.geom.11010H
 Keywords:

 Mathematics  Algebraic Geometry;
 14M25 (Primary);
 52B35 (Secondary)
 EPrint:
 8 pages