Calabi-Yau complete intersections in fake weighted projective spaces

TL;DR

This paper introduces a classification method for Calabi-Yau complete intersections in fake weighted projective spaces, computes their Hodge pairs, and discovers new Hodge pairs not seen in toric hypersurfaces, up to dimension five.

Contribution

It provides a novel classification algorithm for Calabi-Yau complete intersections in fake weighted projective spaces and identifies new Hodge pairs.

Findings

Classified all such complete intersections up to dimension five.

Computed Hodge pairs for 3-dimensional families.

Discovered twenty new Hodge pairs not in toric Calabi-Yau hypersurfaces.

Abstract

We present a classification algorithm for Calabi-Yau complete intersections arising from nef-partitions in fake weighted projective spaces, allowing us to determine all such complete intersections up to dimension five. Furthermore, we compute the Hodge pairs of the $3$-dimensional families obtained, and find twenty new Hodge pairs not realized by any toric Calabi-Yau hypersurface. Finally, we provide an explicit characterization for the families of maximal codimension.