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
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
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