Résume | We analyze the structures that appear on the base-point locus of a net of real quadrics and their relations to real theta-characteristic (in topological term, spin structures) on the corresponding discriminant curves.
The simplest interesting case that will be discussed in the talk is given by the Cayley Octads, that are 8-point intersections of three quadrics in the 3-space.
In the complex setting it is a classical subject studied since 19-th century (Cayley, Hesse, Steiner, etc.) in connection with 27 lines on a cubic, 28 bitangents to a quartic and related objects. In the real setting, Cayley Octads were not however well-studied.
I will start with the deformation classification of real regular Cayley Octads in terms of the corresponding spectral theta-characteristic on the quartics. Next, I will describe the corresponding invariants in terms of eight-point configurations and discuss their
real monodromy groups. |