The Slack Realization Space of a Polytope
Abstract
In this paper we introduce a natural model for the realization space of a polytope up to projective equivalence which we call the slack realization space of the polytope. The model arises from the positive part of an algebraic variety determined by the slack ideal of the polytope. This is a saturated determinantal ideal that encodes the combinatorics of the polytope. We also derive a new model of the realization space of a polytope from the positive part of the variety of a related ideal. The slack ideal offers an effective computational framework for several classical questions about polytopes such as rational realizability, non-prescribability of faces, and realizability of combinatorial polytopes.
Keywords
Cite
@article{arxiv.1708.04739,
title = {The Slack Realization Space of a Polytope},
author = {João Gouveia and Antonio Macchia and Rekha R. Thomas and Amy Wiebe},
journal= {arXiv preprint arXiv:1708.04739},
year = {2019}
}
Comments
The original arXiv submission of this paper has now been split into two parts; this paper describing the slack realization space of a polytope and applications of the slack ideal, and a second paper focussing on toric slack ideals and projective uniqueness