Variety of Power Sums and Divisors in the Moduli Space of Cubic Fourfolds

  • Kristian Ranestad

    Matematisk institutt, Universitetet i Oslo, PO Box 1053 Blindern, NO-0316 Oslo, Norway
  • Claire Voisin

    Collège de France, 3 rue d'Ulm, 75005 Paris, France
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Abstract

We show that a cubic fourfold that is apolar to a Veronese surface has the property that its variety of power sums is singular along a surface of genus 20 which is the variety of power sums of a sextic curve. This relates constructions of Mukai and Iliev and Ranestad. We also prove that these cubics form a divisor in the moduli space of cubic fourfolds and that this divisor is not a Noether-Lefschetz divisor. We use this result to prove that there is no nontrivial Hodge correspondence between a very general cubic and its .

Cite this article

Kristian Ranestad, Claire Voisin, Variety of Power Sums and Divisors in the Moduli Space of Cubic Fourfolds. Doc. Math. 22 (2017), pp. 455–504

DOI 10.4171/DM/571