#### Vol. 299, No. 1, 2019

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Calabi–Yau 4-folds of Borcea–Voisin type from F-theory

### Andrea Cattaneo, Alice Garbagnati and Matteo Penegini

Vol. 299 (2019), No. 1, 1–31
##### Abstract

We apply Borcea–Voisin’s construction and give new examples of Calabi–Yau 4-folds $Y$, which admit an elliptic fibration onto a smooth 3-fold $V$, whose singular fibers of type ${I}_{5}$ lie above a del Pezzo surface $\mathit{dP}\subset V$. These are relevant models for F-theory according to Beasley et al. (2009a, 2009b). Moreover, we give the explicit equations of some of these Calabi–Yau 4-folds and their fibrations.

##### Keywords
Calabi–Yau manifolds, elliptic fibrations, generalized Borcea–Voisin's construction, del Pezzo surfaces, K3 surfaces, F-theory
##### Mathematical Subject Classification 2010
Primary: 14J32, 14J35, 14J50
##### Milestones
Received: 13 July 2017
Revised: 26 February 2018
Accepted: 17 July 2018
Published: 18 April 2019
##### Authors
 Andrea Cattaneo Université Claude Bernard Lyon 1 Institut Camille Jordan Villeurbanne France Alice Garbagnati Dipartimento di Matematica Federigo Enriques Università degli Studi di Milano Milano Italy Matteo Penegini Dipartimento di Matematica - DIMA Università degli Studi di Genova Genova Italy