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Mathematics Subject Classification: 14J70. Secondary 14M15
2010
unpublished
Preserved Fulltext
We show that a cubic fourfold F that is apolar to a Veronese surface has the property that its variety of power sums V SP (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
fatcat:mktlkf2e3fh4xbfgclflzvloya