Non-rational nodal quartic threefolds

dc.creatorCheltsov, Ivan
dc.date2004-05-08
dc.date.accessioned2026-07-07T05:08:03Z
dc.date.available2026-07-07T05:08:03Z
dc.descriptionThe $\mathbb{Q}$-factoriality of a nodal quartic 3-fold implies its non-rationality. We prove that a nodal quartic 3-fold with at most 8 nodes is $\mathbb{Q}$-factorial, and we show that a nodal quartic 3-fold with 9 nodes is not $\mathbb{Q}$-factorial if and only if it contains a plane. However, there are non-rational non-$\mathbb{Q}$-factorial nodal quartic 3-folds in $\mathbb{P}^4$. In particular, we prove the non-rationality of a general non-$\mathbb{Q}$-factorial nodal quartic 3-fold that contains either a plane or a smooth del Pezzo surface of degree 4.
dc.identifierhttps://arxiv.org/abs/math/0405150
dc.identifierhttp://arxiv.org/abs/math/0405150
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71107
dc.subjectAlgebraic Geometry
dc.subject14E08, 14J30, 14J45, 14J70, 14M20
dc.titleNon-rational nodal quartic threefolds
dc.typetext

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