Cremona transformations of plane configurations of 6 points

Abstract

We analyze how a set of 6 points of $RP^2$ in general position changes under quadratic Cremona transformationsbased at triples of points of the given six. As an application, we give an alternative approach to determining thedeformation types (i.e. icosahedral, bipartite, tripartite and hexagonal) of 36 real Schläfli double sixes on any nonsingularreal cubic surface performed by Segre.