论文标题
在瞬间地图和$ g $ varieties的切线捆绑
On moment map and bigness of tangent bundles of $G$-varieties
论文作者
论文摘要
令$ g $为连接的代数组，让$ x $成为平稳的投射$ g $ - 变化。在本文中，我们证明了一个足够的标准，可以使用矩映射$φ_x^g：t^*x \ rightarrow \ mathfrak {g}^*$来确定切线束$ tx $的比格。作为一种应用，验证了某些准同质品种的切线捆绑包的束缚，包括对称品种，霍斯氏质品种和屈服于通勤线性代数群的均值压实。最后，我们详细研究了fano歧管$ x $，带有picard number $ 1 $，这是矢量组$ \ mathbb {g} _a _a^n $的等效压缩。特别是，我们将确定$ \ mathbb {p}（t^*x）$的伪赋锥，并证明沿边界除数$ d $ of $ x $的项目活动矩图的图像在项目上等同于$ x $的VMRT的双重品种。
Let $G$ be a connected algebraic group and let $X$ be a smooth projective $G$-variety. In this paper, we prove a sufficient criterion to determine the bigness of the tangent bundle $TX$ using the moment map $Φ_X^G:T^*X\rightarrow \mathfrak{g}^*$. As an application, the bigness of the tangent bundles of certain quasi-homogeneous varieties are verified, including symmetric varieties, horospherical varieties and equivariant compactifications of commutative linear algebraic groups. Finally, we study in details the Fano manifolds $X$ with Picard number $1$ which is an equivariant compactification of a vector group $\mathbb{G}_a^n$. In particular, we will determine the pseudoeffective cone of $\mathbb{P}(T^*X)$ and show that the image of the projectivised moment map along the boundary divisor $D$ of $X$ is projectively equivalent to the dual variety of the VMRT of $X$.
