Hilbert schemes of finite abelian group orbits and Grobner fans

Details Hilbert schemes of finite abelian group orbits and Grobner fans Hilbert schemes of finite abelian group orbits and Grobner fans

2007-12-18

arxiv.org/abs/0712.2892v1

Mathematics

Algebraic Geometry

13 pages, 3 figures

Scientific paper

Let $G$ be a finite abelian subgroup of
$PGL(r-1,K)=\mathrm{Aut}(\P^{r-1}_K)$. In this paper, we prove that the
normalization of the $G$-orbit 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 $K[x_1, ..., x_r]$.

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