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arXiv:1309.1899 [math.AG]AbstractReferencesReviewsResources

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

Kristian Ranestad, Claire Voisin

Published 2013-09-07, updated 2017-02-11Version 3

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.

Comments: 42 pages, expanded and revised version to appear in Documenta Mathematica
Categories: math.AG
Subjects: 14J70, 14M15, 14N99
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