Algorithms for the Toric Hilbert Scheme

Details Algorithms for the Toric Hilbert Scheme Algorithms for the Toric Hilbert Scheme

2000-10-12

arxiv.org/abs/math/0010130v1

Mathematics

Algebraic Geometry

This is a chapter for the forthcoming book "Computations in Algebraic Geometry using Macaulay 2" edited by D. Eisenbud, D. Gra

Scientific paper

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.

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