Nonexistence of regular maps between homogeneous projective varieties

Author:

Shrawan Kumar

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Group Theory (math.GR), Representation Theory (math.RT)

journal:

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date:

2023-07-12 16:00:00

Abstract

We study non-existence of non-constant regular maps from a partial flag variety $X=G/P$ to another partial flag variety $X'=G'/P'$ 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 $X'=G'/B'$. We also formulate a general conjecture on the non-existence of non-constant regular maps from $X\to X'$.