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

摘要

We show that a cubic fourfold F that is apolar to a Veronese surface has theproperty that its variety of power sums VSP(F,10) is singular along a K3surface of genus 20. We prove that these cubics form a divisor in the modulispace of cubic fourfolds and that this divisor is not a Noether-Lefschetzdivisor. We use this result to prove that there is no nontrivial Hodgecorrespondence between a very general cubic and its VSP.