Resumen de Nonrational nodal quartic threefolds

Ivan Cheltsov

• 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.