期刊
SIAM JOURNAL ON DISCRETE MATHEMATICS
卷 33, 期 3, 页码 1637-1653出版社
SIAM PUBLICATIONS
DOI: 10.1137/18M1233649
关键词
polytopes; slack matrices; slack ideal; realization spaces; realizability; rational realizability
资金
- Centre for Mathematics of the University of Coimbra - Portuguese Government through FCT/MEC [UID/MAT/00324/2013]
- European Regional Development Fund through the Partnership Agreement PT2020
- INdAM
- U.S. National Science Foundation [DMS-1418728]
- NSERC
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, nonprescribability of faces, and realizability of combinatorial polytopes.
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