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arXiv · 1709.00701

Gröbner scheme in the Hilbert scheme and complete intersection monomial ideals

Yuta Kambe
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Abstract

Let $k$ be a commutative ring and $S=k[x_0, \ldots, x_n]$ be a polynomial ring over $k$ with a monomial order. For any monomial ideal $J$, there exists an affine $k$-scheme of finite type, called Gröbner scheme, which parameterizes all homogeneous reduced Gröbner bases in $S$ whose initial ideal is $J$. Here we functorially show that the Gröbner scheme is a locally closed subscheme of the Hilbert scheme if $J$ is a saturated ideal. In the process, we also show that the Gröbner scheme consists of complete intersections if $J$ defines a complete intersection.

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Yuta Kambe. 2019-09-26. Gröbner scheme in the Hilbert scheme and complete intersection monomial ideals. https://arxiv.org/abs/1709.00701

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