Nonrational nodal quartic threefolds

• Autores: Ivan Cheltsov
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 226, Nº 1, 2006, págs. 65-82
• Idioma: inglés
• DOI: 10.2140/pjm.2006.226.65
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• Resumen

  • It is known that the Q-factoriality of a nodal quartic 3-fold in P4 implies its nonrationality. We prove that a nodal quartic 3-fold with at most 8 nodes is Q-factorial, while one with 9 nodes is not Q-factorial if and only if it contains a plane. There are nonrational non-Q-factorial nodal quartic 3-folds. In particular, we prove the nonrationality of a general non-Q-factorial nodal quartic 3-fold that contains either a plane or a smooth del Pezzo surface of degree 4.