Algorithms for the Toric Hilbert Scheme
Algebraic Geometry
2007-05-23 v1 Commutative Algebra
Combinatorics
Abstract
The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vectorspace. All components of the scheme are toric varieties, and among them, there is a fairly well understood coherent component. However, it is unknown whether toric Hilbert schemes are always connected. In this chapter we illustrate the use of Macaulay 2 for exploring the structure of toric Hilbert schemes. In the process we will encounter algorithms from commutative algebra, algebraic geometry, polyhedral theory and geometric combinatorics.
Cite
@article{arxiv.math/0010130,
title = {Algorithms for the Toric Hilbert Scheme},
author = {Michael Stillman and Bernd Sturmfels and Rekha R. Thomas},
journal= {arXiv preprint arXiv:math/0010130},
year = {2007}
}
Comments
This is a chapter for the forthcoming book "Computations in Algebraic Geometry using Macaulay 2" edited by D. Eisenbud, D. Grayson, M. Stillman and B. Sturmfels