横截分层群与构形空间的分层
Groups of Transverse Stratifications and the Hierarchy of Configuration Spaces
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中文总结 AI 辅助
本文引入与模空间横截分层相关的群$G(\boldsymbol{\u0393})$，构造模空间基本群到$G(\boldsymbol{\u0393})$的同态，推广$G_n^k$-理论，讨论横截正则性的例子，研究平面点构形空间的分层并建立二次曲线构形的横截性。
中文摘要 AI 辅助
我们引入了与模空间横截分层相关的一大类群$G(\boldsymbol{\u0393})$。对于满足自然局部条件（横截正则性）的广泛分层类，我们构造了从模空间基本群到对应群$G(\boldsymbol{\u0393})$的同态。这一在配套论文\uc5b4{[Manturov2026]}中证明的一般性定理，对$G_n^k$-理论进行了深远推广。本文的主要目标是讨论横截正则性属性实际出现的众多例子与情形，描述各类具有横截正则性的模空间和分层，尤其研究由代数曲线定义的平面点构形空间的分层，并建立二次曲线构形的横截性属性，在最后一节中阐述了一般分层问题。
英文摘要
We introduce a broad family of groups $G(Γ)$ associated with transverse stratifications of moduli spaces. For a wide class of stratifications satisfying a natural local condition (transverse niceness), we construct a homomorphism from the fundamental group of the moduli space to the corresponding group $G(Γ)$. This general theorem, which is proved in the companion paper \cite{Manturov2026}, provides a far-reaching generalization of the $G_n^k$-theory. The main goal of the present paper is to discuss numerous examples and situations where the transverse niceness property actually occurs. We describe various moduli spaces and stratifications that are transversely nice. In particular, we study the hierarchy of configuration spaces of points in the plane defined by algebraic curves and establish the transversality property for conic configurations. The general hierarchy problem is formulated in the final section.
发表机构
- Moscow Institute of Physics and Technology (MIPT)（莫斯科物理技术学院）
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