Algorithms for the Toric Hilbert Scheme

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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.
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

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Algebraic Geometry, Commutative Algebra, Combinatorics, 14Q, 13P, 5E

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http://salesiana.dossiersoluciones.com/handle/123456789/60117

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0010130
 http://arxiv.org/abs/math/0010130

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arXiv