Bulletin of the
Korean Mathematical Society BKMS

We study the factoriality of a nodal quartic hypersurface $V_4$ in $\mathbb{P}^4$ when there is a hyperplane in $\mathbb{P}^4$ containing all the nodes of $V_4$. As an application, we obtain new examples of irrational quartic $3$-folds.

Keywords: Nodal hypersurface, factoriality, irrationality

MSC numbers: 14C20, 14J17, 14J30

Supported by: The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2021R1F1A1059506) and the Open KIAS Center at Korea Institute for Advanced Study. The second author was supported by the National Research Foundation of Korea(NRF-2020R1A2C1A01008018) and a KIAS Individual Grant (SP037003) via the Center for Mathematical Challenges at Korea Institute for Advanced Study. This research was supported by the Research Grant of Jeonju University in 2021.