论文标题
在一些二次品种的等级指数上
On the rank index of some quadratic varieties
论文作者
论文摘要
关于投影品种$ x \ subset \ mathbb {p}^r $的均质理想的生成结构，我们将$ x $的等级索引定义为最小的整数$ k $，以便$ i（x）$可以由Quadratic tolynomials产生，最多$ k $。最近表明，如果基本场具有特征性$ \ ne 2，3 $，则每个Veronese嵌入式都有排名指数$ 3 $。在本文中，我们介绍了一些基本方法，即当$ x $是其他一些经典的投射品种，例如合理的正常卷轴，Del Pezzo品种，Segre品种和Plücker嵌入，诸如grocation of grastians of Cark索引并找到其值。
Regarding the generating structure of the homogeneous ideal of a projective variety $X \subset \mathbb{P}^r$, we define the rank index of $X$ to be the smallest integer $k$ such that $I(X)$ can be generated by quadratic polynomials of rank at most $k$. Recently it is shown that every Veronese embedding has rank index $3$ if the base field has characteristic $\ne 2, 3$. In this paper, we introduce some basic ways of how to calculate the rank index and find its values when $X$ is some other classical projective varieties such as rational normal scrolls, del Pezzo varieties, Segre varieties and the Plücker embedding of the Grassmannian of lines.
