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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.
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