论文标题
通过单数方案的分布模量
Moduli of Distributions via Singular Schemes
论文作者
论文摘要
令$ x $成为一个平稳的投影品种。我们表明，将$ x $上的编码发行的地图发送给其单数方案，这是分布空间的形态，即希尔伯特计划。我们描述了它的纤维，当$ x = \ mathbb {p}^n $时，通过syzygies计算它们。作为一个应用程序，我们在$ \ mathbb {p}^3 $上描述了1度分布的模量空间。我们还为$ \ Mathbb {p}^3 $的奇异方案的理想提供了最低分级的免费分辨率。
Let $X$ be a smooth projective variety. We show that the map that sends a codimension one distribution on $X$ to its singular scheme is a morphism from the moduli space of distributions into a Hilbert scheme. We describe its fibers and, when $X = \mathbb{P}^n$, compute them via syzygies. As an application, we describe the moduli spaces of degree 1 distributions on $\mathbb{P}^3$. We also give the minimal graded free resolution for the ideal of the singular scheme of a generic distribution on $\mathbb{P}^3$.
