Nonexistence of regular maps between homogeneous projective varieties

Abstract

We study non-existence of non-constant regular maps from a partial flag variety $X=G/P$ to another partial flag variety $X^{\prime }=G^{\prime }/P^{\prime }$ and prove that there does not exist any non-constant regular map from any partial non-complete flag variety $X$ to any complete flag variety $X^{\prime }=G^{\prime }/B^{\prime }$. We also formulate a general conjecture on the non-existence of non-constant regular maps from $X\to X^{\prime }$.

6 pages