Séminaire de Géométrie Tropicale
Mercredi 20 janvier 2016 14h salle 1525-502
Sergey Finashin
(Middle East Technical University, Ankara)
Real Cayley Octads via Spectral Theta-characteristics
Résumé :
Cayley Octads, that are 8-point intersections of three quadrics in 3-space,
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.
An interest to this topic, and more generally, to nets of quadrics in higher dimensions,
in the context of Real Algebraic Geometry has appeared recently.
By Dixon Theorem, studying of nets of quadrics can be reduced to analysis of even non-vanishing theta-characteristics on the spectral
(or discriminant) curve that parameterizes singular quadrics of the net. In particular, in this way one can obtain
deformation classification of real regular Cayley Octads and description of their real monodromy groups that I am going to present.
I will discuss also how the topology of quartic curves is related to the combinatorics of 8-point configurations in the space.