Ciliberto–Di Gennaro conjecture for nodal hypersurfaces
Let be a nodal hypersurface, meaning a hypersurface of degree whose singularities are all ordinary double points. Assume that has at most singular points. Ciliberto–Di Gennaro conjecture. One of the following holds: (1) is factorial; (2) contains a plane and has at least nodes; or (3) contains a quadric surface and has exactly nodes. The conjecture concerns the factoriality of nodal hypersurfaces, a property equivalent here to -factoriality and relevant to questions of rationality. Its status is not resolved in the supplied source context.
References
Primary source
Ksenia Kvitko, “Ciliberto-Di Gennaro conjecture for sextic hypersurfaces”, arXiv:2505.06742 (2025).
Additional references
2 papers in this index state this conjecture (2013–2025). The statement above is taken from the most recent of them; the others are arXiv:1310.0227.
Progress summary
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Solutions 0
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