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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Affine Structures and Non-Archimedean Analytic Spaces
verfasst von : Maxim Kontsevich, Yan Soibelman
Erschienen in: The Unity of Mathematics
Verlag: Birkhäuser Boston
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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 the Homological Mirror conjecture and the 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 two-dimensional sphere
S
2
equipped with naturally defined singular affine structure.