Calabi-Yau 4-folds of Borcea-Voisin type from F-theory
type: Item
instance of: scholarly article
title: Calabi-Yau 4-folds of Borcea-Voisin type from F-theory
zbMATH Open document ID: 1434.14016
author: Andrea Cattaneo
author: Alice Garbagnati
author: Matteo Penegini
published in: Pacific Journal of Mathematics
publication date: 2019-05-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/1706.01689
review text: \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.
reviewed by: Jimmy Dillies
Mathematics Subject Classification ID: 14J32
Mathematics Subject Classification ID: 14J35
Mathematics Subject Classification ID: 14J50
zbMATH DE Number: 7054785
zbMATH Keywords: Calabi-Yau
zbMATH Keywords: Borcea-Voisin
zbMATH Keywords: elliptic fibrations
zbMATH Keywords: F-theory
MaRDI profile type: Publication
OpenAlex ID: W2623040679
arXiv ID: 1706.01689
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Wikidata QID: Q127918328
DOI: 10.2140/PJM.2019.299.1
description: scientific article