Geodesic
Variety of Power Sums and Divisors in the Moduli Space of Cubic Fourfolds
Documenta mathematica, Tome 22 (2017), pp. 455-504.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 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 $VSP$.
Classification : 14J70
Keywords: Waring decomposition 
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     author = {Ranestad, Kristian and Voisin, Claire},
     title = {Variety of {Power} {Sums} and {Divisors} in the {Moduli} {Space} of {Cubic} {Fourfolds}},
     journal = {Documenta mathematica},
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Ranestad, Kristian; Voisin, Claire. Variety of Power Sums and Divisors in the Moduli Space of Cubic Fourfolds. Documenta mathematica, Tome 22 (2017), pp. 455-504. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a38/