Searching for K3 Fibrations

TL;DR

This paper introduces two methods for identifying K3 fibrations in Calabi-Yau manifolds within toric varieties, analyzing over 180,000 spaces and significantly expanding known Hodge number data.

Contribution

The authors develop new techniques to study fibrations in Calabi-Yau manifolds and provide a comprehensive analysis of a large dataset, greatly increasing known Hodge numbers.

Findings

Identified 124,701 K3 fibrations among 184,026 spaces.

Found a total of 167,406 fibrations considering multiple types.

Computed Hodge numbers for many 3-folds, tripling previous data.

Abstract

We present two methods for studying fibrations of Calabi-Yau manifolds embedded in toric varieties described by single weight systems. We analyse 184,026 such spaces and identify among them 124,701 which are K3 fibrations. As some of the weights give rise to two or three distinct types of fibrations, the total number we find is 167,406. With our methods one can also study elliptic fibrations of 3-folds and K3 surfaces. We also calculate the Hodge numbers of the 3-folds obtaining more than three times as many as were previously known.