Strings on Calabi—Yau spaces and toric geometry

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 ≤ 502.