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

Xinyi Fang; Peng Ren

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

Algebraic Geometry 2025-01-08 v2

Authors: Xinyi Fang , Peng Ren

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

Keywords

flag varieties projective varieties vector bundles

Cite

@article{arxiv.2310.08151,
  title  = {Morphisms from $\mathbb{P}^m$ to flag varieties},
  author = {Xinyi Fang and Peng Ren},
  journal= {arXiv preprint arXiv:2310.08151},
  year   = {2025}
}

Comments

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