Calabi-Yau 4-folds of Borcea-Voisin type from F-theory
\textit{C. Borcea} [AMS/IP Stud. Adv. Math. 1, 717--743 (1997; Zbl 0939.14021)] and independently \textit{C. Voisin} [Symétrie miroir. Paris: Société Mathématique de France (1996; Zbl 0849.14001)] introduced a construction to build Calabi-Yau varieties from lower dimensional ones. In this paper, the authors use this construction to build elliptically fibered Calabi-Yau fourfolds which in the language of string theorists is what is called a F-theory. The building blocks in the construction are two \(K3\) surfaces, one of which admits an elliptic fibration. This fibration induces the required fibration on the fourfold. Additionally, they require the second \(K3\) surface to be a double cover of a del Pezzo surface. The key result of the paper is a description of the topology and Hodge diamond of the fourfolds. They also provide a detailed study of the geometry and projective models in specific examples.
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