Variety of power sums and divisors in the moduli space of cubic fourfolds

Kristian Ranestad (1) , Claire Voisin (2)

1 UiO - University of Oslo
2 CMLS - Centre de Mathématiques Laurent Schwartz

We show that a cubic fourfold F that is apolar to a Veronese surface has the property that its variety of power sums VSP(F,10) is singular along a K3 surface of genus 20. We 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 VSP.

Domains: Algebraic Geometry [math.AG]

Kristian Ranestad, Claire Voisin. Variety of power sums and divisors in the moduli space of cubic fourfolds. 2013. ⟨hal-01002965⟩