The universality theorems on the classification problem of configuration varieties and convex polytopes varieties
The universality theorems on the classification problem of configuration varieties and convex polytopes varieties
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DOI：
10.1007/bfb0082792
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
N. Mnev
中科院分区：
文献类型：
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作者：
N. Mnev
结果，我们在这里提出的形式的一部分指导AM Vershic拓扑调查combinatorially定义的配置空间（见他的文章在这卷）。本文将概述两类簇的重合性的证明：第一类是具有某种定向组合型的点构形空间，第二类是有理数上的全半代数簇。(The定向组合型点构形是著名的组合型超平面构形的对偶对象（见[GZ]）。作为推论，我们得到了关于固定组合类型的凸多面体空间的类似事实。这些结果的完整证明包含在作者的论文[M]中。
The results which we present here form the part of guiding by AM Vershic topological investigations of combinatorially defined configuration spaces (see his article in this volume). In this paper we shall outline the proof of coincidence of the two classes of variety: first-the spaces of point configurations in having certain oriented combinatorial type, the second-all semi-algebraic varieties over rational numbers.(The oriented combinatorial type of point configurations is a dual object to the well-known combinatorial type of hyperplane arrangements (see [GZ]).) As a corollary we obtain the similar fact concerning the spaces of convex polytopes of a fixed combinatorial type. The complete proof of these results is contained in the authors thesis [M]•