论文标题
$（2，n）$的固有的grassmanians带有二号的固有grassmannians
Smooth Fano intrinsic Grassmannians of type $(2,n)$ with Picard number two
论文作者
论文摘要
我们介绍了固有的拉格曼尼亚人的概念，该概念概括了众所周知的加权拉格曼尼亚人。固有的grassmannian是一种普通的投射品种，其Cox环由Grassmannian $ \ Mathrm {gr}（d，n）$的plücker理想$ i_ {d，n} $定义。我们对所有平滑的Fano固有的Grassmannians进行了完整的分类，其中包括Picard $（2，N）$，并证明了一个明确的公式，以计算任意$ n $的此类品种的总数。我们研究了它们的几何形状，并表明他们满足了藤田的自由猜想。
We introduce the notion of intrinsic Grassmannians which generalizes the well known weighted Grassmannians. An intrinsic Grassmannian is a normal projective variety whose Cox ring is defined by the Plücker ideal $I_{d,n}$ of the Grassmannian $\mathrm{Gr}(d,n)$. We give a complete classification of all smooth Fano intrinsic Grassmannians of type $(2,n)$ with Picard number two and prove an explicit formula to compute the total number of such varieties for an arbitrary $n$. We study their geometry and show that they satisfy Fujita's freeness conjecture.
