Hokkaido Mathematical Journal

Hilbert schemes of finite abelian group orbits and Gröbner fans

Tomohito MORITA

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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 $K[x_1, \ldots ,x_r]$.

Article information

Source
Hokkaido Math. J., Volume 38, Number 2 (2009), 249-265.

Dates
First available in Project Euclid: 21 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1248190077

Digital Object Identifier
doi:10.14492/hokmj/1248190077

Mathematical Reviews number (MathSciNet)
MR2522914

Zentralblatt MATH identifier
1179.13023

Subjects
Primary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 14E15: Global theory and resolution of singularities [See also 14B05, 32S20, 32S45] 14M25: Toric varieties, Newton polyhedra [See also 52B20]

Keywords
Gröbner fan G-Hilbert schemes toric singularity

Citation

MORITA, Tomohito. Hilbert schemes of finite abelian group orbits and Gröbner fans. Hokkaido Math. J. 38 (2009), no. 2, 249--265. doi:10.14492/hokmj/1248190077. https://projecteuclid.org/euclid.hokmj/1248190077


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