Geodesic
Variety of Power Sums and Divisors in the Moduli Space of Cubic Fourfolds
Documenta mathematica, Tome 22 (2017), pp. 455-504
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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.
DOI : 10.4171/dm/571
Classification : 14J70
Mots-clés : Waring decomposition 
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     author = {Kristian Ranestad and Claire Voisin},
     title = {Variety of {Power} {Sums} and {Divisors} in the {Moduli} {Space} of {Cubic} {Fourfolds}},
     journal = {Documenta mathematica},
     pages = {455--504},
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     doi = {10.4171/dm/571},
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Kristian Ranestad; Claire Voisin. Variety of Power Sums and Divisors in the Moduli Space of Cubic Fourfolds. Documenta mathematica, Tome 22 (2017), pp. 455-504. doi: 10.4171/dm/571

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