Algorithms for the Toric Hilbert Scheme

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dc.creatorStillman, Michael
dc.creatorSturmfels, Bernd
dc.creatorThomas, Rekha R.
dc.date2000-10-12
dc.date.accessioned2026-07-07T04:38:00Z
dc.date.available2026-07-07T04:38:00Z
dc.descriptionThe 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.
dc.descriptionThis 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
dc.identifierhttps://arxiv.org/abs/math/0010130
dc.identifierhttp://arxiv.org/abs/math/0010130
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60117
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subject14Q, 13P, 5E
dc.titleAlgorithms for the Toric Hilbert Scheme
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