Ju n 20 04 Affine structures and non-archimedean analytic spaces
Ju n 20 04 Affine structures and non-archimedean analytic spaces
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Jun n 20 04 仿射结构和非阿基米德解析空间
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发表时间：
2008
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通讯作者：
Y. Soibelman
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作者：
M. Kontsevich;Y. Soibelman
本文提出了一种在非阿基米德域上构造解析空间的方法，从具有仿射结构的真实的流形出发，该流形具有积分单值性。我们的构造是基于同调镜像猜想和几何Strominger-Yau-Zaslow猜想的结合。特别是，我们从“平片”的解析K3曲面。作为我们的方法的副产品，我们得到了一个行动的算术子群的组SO（1，18）的分段线性变换的2维球面S2配备自然定义的奇异仿射结构。
In this paper we propose a way to construct an analytic space over a non-archimedean field, starting with a real manifold with an affine structure which has integral monodromy. Our construction is motivated by the junction of Homological Mirror conjecture and geometric Strominger-Yau-Zaslow conjecture. In particular, we glue from “flat pieces” an analytic K3 surface. As a byproduct of our approach we obtain an action of an arithmetic subgroup of the group SO(1, 18) by piecewise-linear transformations on the 2-dimensional sphere S2 equipped with naturally defined singular affine structure.