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

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 $1\le k\le m-2$.

12 pages, comments are welcome; Updated the reference