Classifying Fibers and Bases in Toric Hypersurface Calabi-Yau Threefolds

TL;DR

This paper provides a comprehensive classification of toric elliptic and genus-one fibrations in all 474 million reflexive polytopes from the Kreuzer-Skarke database, revealing new geometric and physical features relevant to F-theory.

Contribution

It offers the first complete enumeration and analysis of fibrations in the entire Kreuzer-Skarke database, identifying over 2.25 billion equivalence classes and exploring their geometric and physical implications.

Findings

Identified over 2.25 billion fibration classes.

Discovered exotic cases with non-toric bases and high-rank 6D SCFTs.

Illustrated geometric features relevant to F-theory compactifications.

Abstract

We carry out a complete analysis of the toric elliptic and genus-one fibrations of all 474 million reflexive polytopes in the Kreuzer-Skarke database. Earlier work with Huang showed that all but 29,223 of these polytopes have such a fibration. We identify 2,264,992,252 distinct fibrations, and determine the fiber and base structure in each case; after accounting for automorphisms of the ambient polytope, these fibrations furnish 2,250,744,657 equivalence classes. We summarize generic features and identify exotic special cases among these fibrations. These fibrations illustrate many features that have been explored in the context of 6D F-theory, including gauge groups hosted on non-toric divisors, automatic enhancement of gauge groups, and implicit non-toric bases and high-rank 6D SCFTs associated with nonflat fibers, as well as novel geometric features such as singular bases for genus-one fibrations with multisections. This analysis illustrates the power of elliptic and genus-one fibrations, and the geometro-physical language of F-theory as a tool for understanding the structure of Calabi-Yau threefolds.