Description of GL3-orbits on the quadruple projective spaces

Abstract

This paper gives a description of the diagonal [Formula: see text]-orbits on the quadruple projective space [Formula: see text]. 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[Formula: see text] has infinitely many orbits but has also an open orbit in the multiple projective space [Formula: see text].