The Toric Hilbert Scheme of a Rank Two Lattice Is Smooth and Irreducible Diane Maclagan and Rekha R. Thomas
نویسنده
چکیده
The toric Hilbert scheme of a lattice L ⊆ Z is the multigraded Hilbert scheme parameterizing all ideals in k[x1, . . . , xn] with Hilbert function value one for every g in the grading monoid G = N/L. In this paper we show that if L is twodimensional, then the toric Hilbert scheme of L is smooth and irreducible. This result is false for lattices of dimension three and higher as the toric Hilbert scheme of a rank three lattice can be reducible.
منابع مشابه
The toric Hilbert scheme of a rank two lattice is smooth and irreducible
The toric Hilbert scheme of a lattice L ⊆ Z is the multigraded Hilbert scheme parameterizing all ideals in k[x1, . . . , xn] with Hilbert function value one for every g in the grading monoid G = N/L. In this paper we show that if L is twodimensional, then the toric Hilbert scheme of L is smooth and irreducible. This result is false for lattices of dimension three and higher as the toric Hilbert...
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