Description of GL₃-orbits on the quadruple projective varieties

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.2205.07822

Abstract

This article gives a description of the diagonal GL₃-orbits on the quadruple projective variety (\mathbb P²)⁴. We give explicit representatives of orbits, and describe the closure relations of orbits. A distinguished feature of our setting is that it is the simplest case where diag(GL_n) has infinitely many orbits but has an open orbit in the multiple projective space (\mathbb P^n-1)^m.

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