The toric Hilbert scheme of a rank two lattice is smooth and irreducible

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dc.creatorMaclagan, Diane
dc.creatorThomas, Rekha R.
dc.date2002-08-05
dc.date.accessioned2026-07-07T04:50:03Z
dc.date.available2026-07-07T04:50:03Z
dc.descriptionThe 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 grading monoid N^n/L. In this paper we show that if L is two-dimensional, 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.
dc.description19 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0208031
dc.identifierhttp://arxiv.org/abs/math/0208031
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64658
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.titleThe toric Hilbert scheme of a rank two lattice is smooth and irreducible
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