## Hokkaido Mathematical Journal

### Hilbert schemes of finite abelian group orbits and Gröbner fans

Tomohito MORITA

#### 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

https://projecteuclid.org/euclid.hokmj/1248190077

Digital Object Identifier
doi:10.14492/hokmj/1248190077

Mathematical Reviews number (MathSciNet)
MR2522914

Zentralblatt MATH identifier
1179.13023

#### 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