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math.AG2000
Algorithms for the Toric Hilbert Scheme
Michael Stillman, Bernd Sturmfels, Rekha R. Thomas
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…
math.CO2000
Syzygies of Oriented Matroids
I. Novik, A. Postnikov, B. Sturmfels
We construct minimal cellular resolutions of squarefree monomial ideals arising from hyperplane arrangements, matroids and oriented matroids. These are Stanley-Reisner ideals of co…
math.AG2000
Macaulay 2 and the geometry of schemes
Gregory G. Smith, Bernd Sturmfels
This tutorial illustrates how to use Grayson and Stillman's computer algebra system, Macaulay2, to study schemes. The examples are taken from the homework for an algebraic geometry…