Configuration of five points in \mathbb P³ and their limits

2022/05/16 by Shimamoto, Naoya
#14L30 (Primary) #14M15 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2205.07788

Abstract

We give a classification of ordered five points in \mathbb P³ under the diagonal action of GL₄ over an algebraically closed field of characteristic 0, by an explicit description of the diagonal action of GL₄ on the quintuple of the projective varieties \mathbb P³. This is the second simplest setting, where a reductive subgroup of H of G has an open orbit in a (generalised) flag variety X of G but #(H\backslash X)=∞. The closure relations among infinitely many orbits are also given.

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