Gröbner scheme in the Hilbert scheme and complete intersection monomial ideals · arXivDesk1709.00701Sep 3, 2017The contents are completely included in "On the functoriality of marked families"[Paolo Lella, Margherita Roggero]
Gröbner scheme in the Hilbert scheme and complete intersection monomial ideals
Yuta Kambe
Abstract
Let k be a commutative ring and S=k[x0,…,xn] be a polynomial ring over
with a monomial order. For any monomial ideal
, there exists an affine
-scheme of finite type, called Gröbner scheme, which parameterizes all homogeneous reduced Gröbner bases in
whose initial ideal is
. Here we functorially show that the Gröbner scheme is a locally closed subscheme of the Hilbert scheme if
is a saturated ideal. In the process, we also show that the Gröbner scheme consists of complete intersections if
defines a complete intersection.