# Bulletin of theKorean Mathematical SocietyBKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc.

Published online August 24, 2021

## Some irrational quartic threefolds

Kyusik Hong and Joonyeong Won

Jeonju University, KIAS

### Abstract

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