Planes in cubic fourfolds

Abstract: We discuss possible numbers of 2-planes in a smooth cubic hypersurface in the 5-dimensional projective space. We show that, in the complex case, the maximal number of planes is 405, the maximum being realized by the Fermat cubic. In the real case, the maximal number of planes is 357. The proofs deal with the period spaces of cubic hypersurfaces in the 5-dimensional complex projective space and are based on the global Torelli theorem and the surjectivity of the period map for these hypersurfaces, as well as on Nikulin's theory of discriminant forms. Joint work with Alex Degtyarev and John Christian Ottem.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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