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Morphisms from $\mathbb{P}^m$ to flag varieties

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arxiv 2310.08151 v2 pith:2JRGIKIH submitted 2023-10-12 math.AG

Xinyi Fang , Peng Ren This is my paper · ORCID
classification math.AG
keywords morphismsdotsflagmathbbvarietiesbundlesconditionsconsequence
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abstract

In this paper, we consider the morphisms from projective spaces to flag varieties. We show that the morphisms can only be constant under some special conditions. As a consequence, we prove that the splitting types of unsplit uniform $r$-bundles on $\mathbb{P}^m$ can not be $(a_1,\dots,a_1,a_2,\dots,a_{r-k+1})$ for $1\le k\le m-2$.

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