2004/05/08 by Ivan Cheltsov, Cheltsov, Ivan · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #math.AG #msc:14E08 #msc:14J30 #msc:14J45 #msc:14J70 #msc:14M20
paper · pdf · doi:10.48550/arxiv.math/0405150
arxiv created 2004/05/08 · arxiv updated 2009/12/01
The 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 ℚ-factorial, and we show that a nodal quartic 3-fold with 9 nodes is not ℚ-factorial if and only if it contains a plane. However, there are non-rational non-ℚ-factorial nodal quartic 3-folds in ℙ4. In particular, we prove the non-rationality of a general non-ℚ-factorial nodal quartic 3-fold that contains either a plane or a smooth del Pezzo surface of degree 4.