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

DOI: 10.2140/pjm.2019.299.1

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