Real Algebraic and Analytic Geometry |

Mild Manifolds and a Non-Standard Riemann Existence Theorem.

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Submission: 2008, January 29.

*Abstract:
Let R be an o-minimal expansion of a real closed field whose
algebraic closure (in the sense of fields) is K.
In earlier papers we investigated the notions of
R-definable K-holomorphic maps, K-analytic manifolds and their
K-analytic subsets. We call such a K-manifold mild if it eliminates
quantifiers after endowing it with all K-analytic subsets. Examples are
compact complex manifolds and non-singular algebraic curves over K.
We examine here basic properties of mild manifolds and prove that when
a mild manifold M is strongly minimal and not locally modular then M is
bi-holomorphic with a non-singular algebraic curve over K.*

Mathematics Subject Classification (2000): 03C64, 03H05, 32P05, 03C98, 30F99, 32C25.

Keywords and Phrases: O-minimality, Non-Archimedean complex analysis, Zariski geometries, Riemann existence theorem.

**Full text**, 24p.:
pdf 996k.

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