纤维化与代数约化的若干模型论
逻辑
2013-12-19 v2 复变函数
摘要
设p=tp(a/A)是任意有限秩稳定理论中的平稳类型，P是A不变的部分类型族。引入并刻画了以下性质：只要c在(A,a)上可定义且a在(A,c)上非代数，则tp(c/A)几乎内在于P。该刻画涉及平稳类型的一个看似新的“下降”概念。动机部分来自[Campana, Oguiso, and Peternell. Non-algebraic hyperkähler manifolds. Journal of Differential Geometry, 85(3):397–424, 2010]第2节的结果，其中给出了广义超凯勒流形的结构性质。本文获得的模型论结果被应用于复解析环境，证明非代数（广义）超凯勒流形的代数约化不下降。这些结果也应用于微分闭域理论，并给出了来自微分代数群的例子。
引用
@article{arxiv.1210.2793,
title = {Some model theory of fibrations and algebraic reductions},
author = {Rahim Moosa and Anand Pillay},
journal= {arXiv preprint arXiv:1210.2793},
year = {2013}
}
备注
Substantially revised and augmented. A new section applying the results to differentially closed fields has been added; title, abstract, and introduction are new, and several new examples are added. 14 pages