模型论眼中的全纯阴影
Holomorphic shadows in the eyes of model theory
摘要：
定义了殆复流形（M，J）的一个子集为全纯影，如果它是紧致复流形的J-全纯映射的像.注意J-全纯曲线是全纯阴影，紧复流形的复子簇也是。证明了在一定条件下，流形M上的殆复结构J上的全纯阴影在（M，J）的笛卡儿积中形成Zapriki型结构.检查这导致非平凡的几何问题和结果。然后，我们将Hrushovski和Zilber的工作应用于Zurki型结构。我们还重述了Gromov和McDuff关于辛几何中J-全纯曲线的结果。
英文摘要：
We define a subset of an almost complex manifold (M,J) to be a holomorphic shadow if it is the image of a J-holomorphic map from a compact complex manifold. Notice that a J-holomorphic curve is a holomorphic shadow, and so is a complex subvariety of a compact complex manifold. We show that under some conditions on an almost complex structure J on a manifold M, the holomorphic shadows in the Cartesian products of (M,J) form a Zariski-type structure. Checking this leads to non-trivial geometric questions and results. We then apply the work of Hrushovski and Zilber on Zariski-type structures. We also restate results of Gromov and McDuff on J-holomorphic curves in symplectic geometry in the language of shadows structures.
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