Strings on Calabi--Yau spaces and Toric Geometry

TL;DR

This paper reviews the use of toric geometry in classifying Calabi-Yau hypersurfaces and complete intersections, highlighting the current understanding of Hodge number bounds within string theory contexts.

Contribution

It provides a comprehensive review of toric Calabi-Yau hypersurfaces and presents new data on complete intersections, emphasizing the bounded nature of Hodge numbers.

Findings

All new data on Calabi-Yau spaces stay within the range h11+h12 ≤ 502.

No proof exists for a finite bound on Hodge numbers.

The paper discusses the role of toric geometry in string dualities.

Abstract

After a brief introduction into the use of Calabi--Yau varieties in string dualities, and the role of toric geometry in that context, we review the classification of toric Calabi-Yau hypersurfaces and present some results on complete intersections. While no proof of the existence of a finite bound on the Hodge numbers is known, all new data stay inside the familiar range $h_{11}+h_{12}\le 502$.