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- W3042885153 abstract "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 $delta_i$-unstable for some $delta_i$. So we partially answer a problem posted by Mu~{n}oz-Occhetta-Sol'{a} 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 Mu~{n}oz-Occhetta-Sol'{a} 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-M{u}lich-Barth theorem on rational homogeneous spaces." @default.
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- W3042885153 date "2020-07-14" @default.
- W3042885153 modified "2023-09-24" @default.
- W3042885153 title "Vector Bundles on Rational Homogeneous Spaces" @default.
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- W3042885153 doi "https://doi.org/10.48550/arxiv.2007.06816" @default.
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