Real deformations of Cayley octads and their links

Cayley octads are 8-configurations in $P^3$ that are complete intersections of three quadrics (i.e., the base locus of a net of quadrics). The locus formed by singular quadrics of the net form a Hessian (or spectral) quartic endowed with an even theta characteristic. An octad is called regular if this quartic is non-singular. Using this correspondence one can obtain a deformation classification of real regular Cayley octads which will be discussed. Namely, I will present the 8 deformation classes of maximal real regular Cayley octads and discuss their monodromy groups and degenerations. I will relate also Cayley octads with the 14 real deformation classes of 7-configurations (Aronhold sets) which appear to be their links.