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May 2009 Hilbert schemes of finite abelian group orbits and Gröbner fans
Tomohito MORITA
Hokkaido Math. J. 38(2): 249-265 (May 2009). DOI: 10.14492/hokmj/1248190077

Abstract

Let $G$ be a finite abelian subgroup of $PGL(r1,K)=\mathrm{Aut}(\mathbb{P}^{r-1}_K)$. In this paper, we prove that the normalization of the $G$-Hilbert scheme$Hilb^G(\mathbb{P}^{r-1})$ is described as a toric variety, which corresponds to the Gröbner fan for some homogeneous ideal $I$ of $K[x_1, \ldots ,x_r]$.

Citation

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Tomohito MORITA. "Hilbert schemes of finite abelian group orbits and Gröbner fans." Hokkaido Math. J. 38 (2) 249 - 265, May 2009. https://doi.org/10.14492/hokmj/1248190077

Information

Published: May 2009
First available in Project Euclid: 21 July 2009

zbMATH: 1179.13023
MathSciNet: MR2522914
Digital Object Identifier: 10.14492/hokmj/1248190077

Subjects:
Primary: 13P10
Secondary: 14E15, 14L30, 14M25

Rights: Copyright © 2009 Hokkaido University, Department of Mathematics

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Vol.38 • No. 2 • May 2009
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