Published January 1, 2023 | Version v1
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Planes in cubic fourfolds

  • 1. Bilkent Univ, Dept Math, TR-06800 Ankara, Turkiye
  • 2. Univ Oslo, Dept Math, Box 1053, N-0316 Oslo, Norway

Description

We show that the maximal number of planes in a complex smooth cubic fourfold in P5 is 405, realized by the Fermat cubic only; the maximal number of real planes in a real smooth cubic fourfold is 357, realized by the so-called Clebsch-Segre cubic. Altogether, there are but three (up to projective equivalence) cubics with more than 350 planes.

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