Variety of Power Sums and Divisors in the Moduli Space of Cubic Fourfolds
نویسنده
چکیده
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 correspondence between a very general cubic and its V SP .
منابع مشابه
Kodaira Dimension of Moduli of Special Cubic Fourfolds
A special cubic fourfold is a smooth hypersurface of degree three and dimension four that contains a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a countable family of Noether-Lefschetz divisors Cd in the moduli space C of smooth cubic fourfolds. These divisors are irreducible 19-dimensional varieties birational to certain orthogonal modular varieties....
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