Title of Seminar: Algebraic Geometry Preprint Seminar 2025
Title of Talk: Morphism between homogeneous varieties
Speaker: A.J. Parameswaran, TIFR, Mumbai
Date: October 03, 2023
Time: 16:00:00 Hours
Venue: AG-77

Abstract: There are many classical and obvious results on morphisms: like $\mathbb{P}^n$ cannot map (nonconstant) to $\mathbb{P}^m$ if $m < n$, every nonconstant map of $\mathbb{P}^n$ is finite and so on. We will racall some results of Tango on morphisms of Grassmannians. We will sketch a proof of the fact that every map of $\mathbb{P}^2$ to $\mathrm{SL}_{n/B}$ is constant and conclude that if $\mathrm{SL}_{n/P}$ to $\mathrm{SL}_{m/B}$ is a nonconstant map then the parabolic $P$ is a Borel subgroup of $\mathrm{SL}_n$. We will extend this to showing some examples of maps of $\mathbb{P}^3$ to homogeneous spaces by minimal parabolic subgroups and draw the attention to the recent conjecture of Shrawan Kumar.