تقرير
Gr\'obner scheme in the Hilbert scheme and complete intersection monomial ideals
| العنوان: | Gr\'obner scheme in the Hilbert scheme and complete intersection monomial ideals |
|---|---|
| المؤلفون: | Kambe, Yuta |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra, 14C05, 13P10, 13F20 |
| الوصف: | 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 Gr\"obner scheme, which parameterizes all homogeneous reduced Gr\"obner bases in $S$ whose initial ideal is $J$. Here we functorially show that the Gr\"obner scheme is a locally closed subscheme of the Hilbert scheme if $J$ is a saturated ideal. In the process, we also show that the Gr\"obner scheme consists of complete intersections if $J$ defines a complete intersection. Comment: The contents are completely included in "On the functoriality of marked families"[Paolo Lella, Margherita Roggero] |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1709.00701 |
| رقم الأكسشن: | edsarx.1709.00701 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |