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In our previous works we have classified real non-singular cubichypersurfaces in the 5-dimensional projective space up to equivalence thatincludes both real projective transformations and continuous variations ofcoefficients preserving the hypersurface non-singular. Here, we perform a finerclassification giving a full answer to the chirality problem: which of realnon-singular cubic hypersurfaces can not be continuously deformed to theirmirror reflection.

Chirality of Real Non-singular Cubic Fourfolds and Their Pure Deformation Classification