THE SLACK REALIZATION SPACE OF A POLYTOPE
THE SLACK REALIZATION SPACE OF A POLYTOPE
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DOI：
10.1137/18m1233649
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发表时间：
2019-01-01
影响因子：
0.8
通讯作者：
Wiebe, Amy
中科院分区：
文献类型：
--
作者：
Gouveia, Joao;Macchia, Antonio;Wiebe, Amy
在本文中，我们介绍了一个自然的模型，实现空间的多面体投影等价，我们称之为松弛实现空间的多面体。该模型源于由多面体的松弛理想确定的代数簇的正部分。这是一个饱和的行列式理想，它对多面体的组合进行编码。我们还从一个相关理想的簇的正部分导出了一个新的多面体的实现空间模型。松弛理想提供了一个有效的计算框架，如合理的可实现性，nonprescribability的脸，组合多面体的可实现性的几个经典问题的多面体。
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.