On the Hodge structure of elliptically fibered Calabi-Yau threefolds

TL;DR

This paper explores the Hodge structure of elliptically fibered Calabi-Yau threefolds, revealing bounds and geometric properties influenced by F-theory and the minimal model program, with implications for string theory compactifications.

Contribution

It establishes a rigorous upper bound on the Hodge number h_{21} and connects geometric structures to physical models, expanding understanding of Calabi-Yau threefolds in string theory.

Findings

Hodge numbers fill out the 'shield' structure.

Bound on h_{21} is <= 491.

Largest Hodge numbers linked to specific toric base blow-ups.

Abstract

The Hodge numbers of generic elliptically fibered Calabi-Yau threefolds over toric base surfaces fill out the "shield" structure previously identified by Kreuzer and Skarke. The connectivity structure of these spaces and bounds on the Hodge numbers are illuminated by considerations from F-theory and the minimal model program. In particular, there is a rigorous bound on the Hodge number h_{21} <= 491 for any elliptically fibered Calabi-Yau threefold. The threefolds with the largest known Hodge numbers are associated with a sequence of blow-ups of toric bases beginning with the Hirzebruch surface F_{12} and ending with the toric base for the F-theory model with largest known gauge group.