Computational procedures for weighted projective spaces

TL;DR

This paper introduces computational procedures in Maple for analyzing weighted projective spaces, including generating toric data, recognizing weights from fans or polytopes, and converting between these representations.

Contribution

It provides novel algorithms for identifying weights and converting between polytopes and fans in the context of weighted projective spaces.

Findings

Procedures to produce toric data for weighted projective spaces.

Algorithms to recognize weights from fans or polytopes.

Methods to connect polytopes and fans in weighted projective spaces.

Abstract

This is a pdf print of the homonymous Maple file, freely available at http://www.maplesoft.com/applications/view.aspx?SID=127621, providing procedures which are able to produce the toric data associated with a (polarized) weighted projective space i.e. fans, polytopes and their equivalences. More originally it provides procedures which are able to detect a weights vector Q starting from either a fan or a polytope: we will call this process the recognition of a (polarized) weighted projective space. Moreover it gives procedures connecting polytopes of a polarized weighted projective space with an associated fan and viceversa.