Seminar in Real and Complex Geometry

Thursday, March 28, 2019, 16:00-18:00, Schreiber building, room 209

Viatcheslav Kharlamov (Université de Strasbourg)

Deformation chirality of real cubic fourfolds


We call a real non-singular projective variety chiral if it is not deformation equivalent to its image under a mirror reflection. Such a phenomenon may show its up only in projective spaces of odd dimension. The simplest, and the only studied completely, case was that of degree 4 surfaces in the 3-space. A few years ago, in a joint work with S. Finashin, we have elaborated an approach reducing the problem of chirality of real cubic fourfolds to arithmetics of lattices associated with the action of the complex conjugation in the homology of a cubic fourfold. The aim of my talk is to present a full answer that we have now obtained following this approach.