## MORITA Tomohito,

## Hilbert schemes of finite abelian group orbits and Gr\"obner fans.

## Hokkaido Mathematical Journal, 38 (2009) pp.249-265

### Fulltext

PDF### Abstract

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

MSC(Primary) | 13P10 |
---|---|

MSC(Secondary) | 14L30, 14E15, 14M25 |

Uncontrolled Keywords | Gr\"obner fan, G-Hilbert schemes, toric singularity. |