PALP - a User Manual

TL;DR

PALP 2.1 provides a comprehensive toolkit for toric geometry and Calabi–Yau constructions, detailing five executables that handle polytopes, nef partitions, and Mori cones. The manual emphasizes input formats, error handling, and the interplay between M- and N-lattices, with new capabilities such as Mori-cone computations and reflexive Gorenstein-cone analysis. It showcases workflows for extracting topological data (Hodge numbers, Euler characteristics, intersection rings) via SINGULAR DGPS, and highlights integration with Sage and public repositories. The practical impact lies in enabling robust, cross-checked toric data pipelines for Calabi–Yau and related geometries, suitable for both mathematical classification and string-theory applications. All mathematical notation is presented with explicit delimiters to support precise computational interpretations.

Abstract

This article provides a complete user's guide to version 2.1 of the toric geometry package PALP by Maximilian Kreuzer and others. In particular, previously undocumented applications such as the program nef.x are discussed in detail. New features of PALP 2.1 include an extension of the program mori.x which can now compute Mori cones and intersection rings of arbitrary dimension and can also take specific triangulations of reflexive polytopes as input. Furthermore, the program nef.x is enhanced by an option that allows the user to enter reflexive Gorenstein cones as input. The present documentation is complemented by a Wiki which is available online.