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arXiv · 1703.05923

Some non-special cubic fourfolds

Nicolas Addington·Asher Auel
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Abstract

In [1309.1899], Ranestad and Voisin showed, quite surprisingly, that the divisor in the moduli space of cubic fourfolds consisting of cubics "apolar to a Veronese surface" is not a Noether-Lefschetz divisor. We give an independent proof of this by exhibiting an explicit cubic fourfold X in the divisor and using point counting methods over finite fields to show X is Noether-Lefschetz general. We also show that two other divisors considered in [ibid.] are not Noether-Lefschetz divisors.

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Nicolas Addington, Asher Auel. 2017-03-17. Some non-special cubic fourfolds. https://doi.org/10.25537/dm.2018v23.637-651

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