Nonrational nodal quartic threefolds

Ivan Cheltsov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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

Original languageEnglish
Pages (from-to)65-81
Number of pages17
JournalPacific Journal of Mathematics
Issue number1
Publication statusPublished - 1 Jul 2006

Keywords / Materials (for Non-textual outputs)

  • del Pezzo surface
  • Fano variety
  • Nodal variety
  • Quartic threefold
  • Q{double-struck}-factorial


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