Toric complete intersections and weighted projective space
Maximilian Kreuzer, Erwin Riegler, David Sahakyan
TL;DR
This work extends the Batyrev–Borisov nef-partition approach to toric complete intersections, providing a computational framework to derive Hodge data via Gorenstein cones and Eulerian-poset polynomials. By systematically constructing nef partitions of reflexive polytopes and comparing with weighted projective space realizations, the authors recover many known cases and uncover numerous new Calabi–Yau spectra, including $87$ novel Hodge-number pairs (primarily with $h^{11}\le 4$) and $16$–$32$ new spectra via nef partitions. The results demonstrate the effectiveness of toric nef-partitions for generating and classifying mirror pairs of complete intersections and highlight the interplay between toric geometry and weighted-projective realizations. The work broadens the landscape of Calabi–Yau manifolds with computable mirror data and provides practical tools for exploring mirror symmetry in codimension greater than one.
Abstract
It has been shown by Batyrev and Borisov that nef partitions of reflexive polyhedra can be used to construct mirror pairs of complete intersection Calabi--Yau manifolds in toric ambient spaces. We construct a number of such spaces and compute their cohomological data. We also discuss the relation of our results to complete intersections in weighted projective spaces and try to recover them as special cases of the toric construction. As compared to hypersurfaces, codimension two more than doubles the number of spectra with $h^{11}=1$. Alltogether we find 87 new (mirror pairs of) Hodge data, mainly with $h^{11}\le4$.