All Complete Intersection Calabi-Yau Four-Folds

TL;DR

This paper provides an exhaustive classification of complete intersection Calabi-Yau four-folds, listing over 900,000 configurations, most of which are elliptically fibered and relevant for F-theory models.

Contribution

It offers the first comprehensive, constructive catalog of all topologically distinct complete intersection Calabi-Yau four-folds in products of projective spaces.

Findings

921,497 configuration matrices identified

Manifolds have Euler characteristics from 0 to 2610

Nearly all are elliptically fibered

Abstract

We present an exhaustive, constructive, classification of the Calabi-Yau four-folds which can be described as complete intersections in products of projective spaces. A comprehensive list of 921,497 configuration matrices which represent all topologically distinct types of complete intersection Calabi-Yau four-folds is provided and can be downloaded at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html . The manifolds have non-negative Euler characteristics in the range 0 - 2610. This data set will be of use in a wide range of physical and mathematical applications. Nearly all of these four-folds are elliptically fibered and are thus of interest for F-theory model building.