Diophantine geometry over groups I: Makanin-Razborov diagrams
Diophantine geometry over groups I: Makanin-Razborov diagrams
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I 组上的丢番图几何：Makanin-Razborov 图
DOI：
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发表时间：
2001
期刊：
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通讯作者：
Z. Sela
中科院分区：
文献类型：
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作者：
Z. Sela
本文是关于自由群中方程组解集的结构、此类集合的投影以及在自由群上定义的基本集结构的系列文章中的第一篇。在第一篇论文中，我们提出了（规范的）Makanin-Razborov 图，它编码了方程组的解集。我们继续研究解集的参数族，并将规范的分级 Makanin-Razborov 图与这样的族关联起来，该图对与参数族中的各个成员相关联的 Makanin-Razborov 图的集合进行编码。
This paper is the first in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the first paper we present the (canonical) Makanin-Razborov diagram that encodes the set of solutions of a system of equations. We continue by studying parametric families of sets of solutions, and associate with such a family a canonical graded Makanin-Razborov diagram, that encodes the collection of Makanin-Razborov diagrams associated with the individual members in the parametric family.