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math.AG2002
The toric Hilbert scheme of a rank two lattice is smooth and irreducible
Diane Maclagan, Rekha R. Thomas
The toric Hilbert scheme of a lattice L in Z^n is the multigraded Hilbert scheme parameterizing all ideals in k[x_1,...,x_n] with Hilbert function value one for every degree in the…
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.AG1999
Combinatorics of the toric Hilbert scheme
Diane Maclagan, Rekha R. Thomas
The toric Hilbert scheme is a parameter space for all ideals with the same multi-graded Hilbert function as a given toric ideal. Unlike the classical Hilbert scheme, it is unknown…