A new offspring of PALP

TL;DR

The paper introduces mori.x, a PALP component for constructing and analyzing Calabi-Yau threefold hypersurfaces in toric ambient spaces determined by reflexive polytopes. Its main approach combines crepant star triangulations to resolve ambient spaces, the Oda-Park algorithm to determine the Mori cone, and SINGULAR DGPS to compute intersection rings and characteristic classes, enabling CY (and non-CY) hypersurface analysis. Key contributions include integrating Mori cone computation, Kreuzer polynomial representation, and topological data extraction within a single tool, with outputs such as Hodge numbers $h^{1,1}$, $h^{2,1}$ and Euler characteristic for CY cases. The work provides a practical, SIG-intensive resource for string-theory model building and systematic exploration of toric Calabi-Yau geometries, leveraging a dual pair of reflexive polytopes $(P, P^*)$ and supporting both subset CY and non-CY analyses under precise triangulation and input formats.

Abstract

We describe the C program mori.x. It is part of PALP, a package for analyzing lattice polytopes. Its main purpose is the construction and analysis of three--dimensional smooth Calabi--Yau hypersurfaces in toric varieties. The ambient toric varieties are given in terms of fans over the facets of reflexive lattice polytopes. The program performs crepant star triangulations of reflexive polytopes and determines the Mori cones of the resulting toric varieties. Furthermore, it computes the intersection rings and characteristic classes of hypersurfaces.