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Bull. Korean Math. Soc. 2022; 59(2): 361-373

Published online March 31, 2022 https://doi.org/10.4134/BKMS.b210158

Copyright © The Korean Mathematical Society.

Some irrational quartic threefolds

Kyusik Hong, Joonyeong Won

Jeonju University; Ewha Womans University

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

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