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arXiv · 0712.2892

Hilbert schemes of finite abelian group orbits and Grobner fans

Tomohito Morita
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Abstract

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

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Tomohito Morita. 2007-12-18. Hilbert schemes of finite abelian group orbits and Grobner fans. https://arxiv.org/abs/0712.2892

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