Geodesic
Some Non-Special Cubic Fourfolds
Documenta mathematica, Tome 23 (2018), pp. 637-651
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In [20], 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 [20] are not Noether–Lefschetz divisors.
DOI : 10.4171/dm/628
Classification : 14C30, 14D10, 14G10, 14G15, 14J10, 14J28, 14J35, 14Q15
Mots-clés : Zeta functions, Noether-Lefschetz loci, cubic fourfolds, computation 
@article{10_4171_dm_628,
     author = {Nicolas Addington and Asher Auel},
     title = {Some {Non-Special} {Cubic} {Fourfolds}},
     journal = {Documenta mathematica},
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     year = {2018},
     volume = {23},
     doi = {10.4171/dm/628},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/628/}
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Nicolas Addington; Asher Auel. Some Non-Special Cubic Fourfolds. Documenta mathematica, Tome 23 (2018), pp. 637-651. doi: 10.4171/dm/628

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