hypersurfaces in P^5 containing unexpected subvarieties

I. Vainsencher

Journal of Singularities
volume 9 (2014), 219-225

Received 16 April 2012. Received in revised form 1 February 2013.

DOI: 10.5427/jsing.2014.9q

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Smooth cubic 4-folds in P^5 containing a general pair of 2-planes are known to be rational. They form a family of codimension 2 in P^{55}. We find a polynomial which encodes, for all d>2, the degrees of the loci of hypersurfaces in P^5 of degree d containing some plane-pair.


intersection theory, Noether-Lefschetz locus, enumerative geometry, rational cubic fourfold

Mathematical Subject Classification:

14N05, 14N15

Author(s) information:

I. Vainsencher
Departamento de Matemática
Belo Horizonte, MG, Brazil
email: israel@mat.ufmg.br