论文标题
矢量束在合理均匀的空间上
Vector Bundles on Rational Homogeneous Spaces
论文作者
论文摘要
我们考虑一个均匀的$ r $ -Bundle $ e $在复杂的合理均匀空间上$ x $ x $ x $ x $ x $ field $ \ mathbb {c} $ 并表明，如果$ e $相对于所有特殊线条的多均匀统一，而排名$ r $仅或等于某些仅取决于$ x $的数字，则$ e $是直接的线条捆绑包或$Δ_i$ - $Δ_i$ - unstable对于某些$Δ_I$。因此，我们部分回答了Muñoz-Occhetta-SoláConde发布的问题。特别是，如果$ x $是广义的Grassmannian $ \ Mathcal {g} $，并且等级$ r $小于或等于仅取决于$ x $的某些数字，则$ e $ split作为直接的线条捆绑包。当$ x $是一种普遍的grassmannian时，我们改善了Muñoz-Occhetta-SoláConde的主要定理，考虑了Chow戒指。此外，通过计算两个合理均匀空间之间的相对切线捆绑，我们为有理均匀空间的广义grauert-mülich-barth定理提供了明确的界限。
We consider a uniform $r$-bundle $E$ on a complex rational homogeneous space $X$ %over complex number field $\mathbb{C}$ and show that if $E$ is poly-uniform with respect to all the special families of lines and the rank $r$ is less than or equal to some number that depends only on $X$, then $E$ is either a direct sum of line bundles or $δ_i$-unstable for some $δ_i$. So we partially answer a problem posted by Muñoz-Occhetta-Solá Conde. In particular, if $X$ is a generalized Grassmannian $\mathcal{G}$ and the rank $r$ is less than or equal to some number that depends only on $X$, then $E$ splits as a direct sum of line bundles. We improve the main theorem of Muñoz-Occhetta-Solá Conde when $X$ is a generalized Grassmannian by considering the Chow rings. Moreover, by calculating the relative tangent bundles between two rational homogeneous spaces, we give explicit bounds for the generalized Grauert-Mülich-Barth theorem on rational homogeneous spaces.
