• Bulletin of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.361-373
• /
• 2022

We study the factoriality of a nodal quartic hypersurface V₄ in ℙ⁴ when there is a hyperplane in ℙ⁴ containing all the nodes of V₄. As an application, we obtain new examples of irrational quartic 3-folds.

• The Pure and Applied Mathematics
• /
• v.29 no.2
• /
• pp.201-206
• /
• 2022

Let X be a nodal complete intersection 3-fold defined by a hypersurface in ℙ⁵ of degree n and a smooth quadratic hypersurface in ℙ⁵ . Then we show that X is factorial if it has at most n² - n + 1 nodes and contains no 2-planes, where n = 3, 4.