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Article overview
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Algorithms for the Toric Hilbert Scheme | Michael Stillman
; Bernd Sturmfels
; Rekha R. Thomas
; | Date: |
13 Oct 2000 | Subject: | Algebraic Geometry; Combinatorics; Commutative Algebra MSC-class: 14Q, 13P, 5E | math.AG math.AC math.CO | Affiliation: | Cornell U.), Bernd Sturmfels (UC Berkeley) and Rekha R. Thomas (U. of Washington | 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. | Source: | arXiv, math.AG/0010130 | Services: | Forum | Review | PDF | Favorites |
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