论文标题
$ g $ -bott-bott-samelson-demazure-Hansen品种的线捆
Line bundles on $G$-Bott-Samelson-Demazure-Hansen varieties
论文作者
论文摘要
让$ g $是半简单的一个半简单的代数组，即在代数封闭的$ k $的任意特征上连接。令$ b $是$ g $的borel子组，其中包含最大圆环$ t $ $g。$ $ w $是$ g $的weyl of $ g $相对于$ t $。对于任意序列$ w =（s_ {i_ {1}}，s_ {i_ {2}}，\ ldots，s_ {i_ {r}} $ in $ w，$ w，$ w，$ z__ {w}的简单反思$是bott-samelson-demelson-demelson-demerson-demazure-hansen proveration $ bs bsdh-word fort y。美元成为fano（弱者）。我们表明，仅当它是nef时，全局生成了$ z_ {w} $上的线捆绑包。我们表明Picard group $ \ text {pic}（\ widetilde {z__ {w}}）$是免费的abelian，我们构造了$ \ mathcal {o}（1）$ - 基础。我们在$ \ widetilde上表征了NEF，全球生成，充足和非常丰富的线捆绑，以$ \ Mathcal {o}（1）$ - 基础为$ \ wideTilde {z_ {w}} $。
Let $G$ be a semi-simple simply connected algebraic group over an algebraically closed field $k$ of arbitrary characteristic. Let $B$ be a Borel subgroup of $G$ containing a maximal torus $T$ of $G.$ Let $W$ be the Weyl group of $G$ with respect to $T$. For an arbitrary sequence $w=(s_{i_{1}},s_{i_{2}},\ldots, s_{i_{r}})$ of simple reflections in $W,$ let $Z_{w}$ be the Bott-Samelson-Demazure-Hansen variety (BSDH-variety for short) corresponding to $w.$ Let $\widetilde{Z_{w}}:=G\times^{B}Z_{w}$ denote the fibre bundle over $G/B$ with the fibre over $B/B$ is $Z_{w}.$ In this article, we give necessary and sufficient conditions for the varieties $Z_{w}$ and $\widetilde{Z_{w}}$ to be Fano (weak-Fano). We show that a line bundle on $Z_{w}$ is globally generated if and only if it is nef. We show that Picard group $\text{Pic}(\widetilde{Z_{w}})$ is free abelian and we construct a $\mathcal{O}(1)$-basis. We characterize the nef, globally generated, ample and very ample line bundles on $\widetilde{Z_{w}}$ in terms of the $\mathcal{O}(1)$-basis.
