论文标题
判别品种补充的Cech封面。第二部分：高斯 - 斯基兹兹的变形
Cech cover of the complement of the discriminant variety. Part II: Deformations of Gauss-skizze
论文作者
论文摘要
考虑了$ n $标记点的配置空间。我们通过所谓的高斯 - 基兹兹（Gauss-Skizze），即高斯（Gauss）引入的森林，研究了这个空间的分解。事实证明，这种分解是半代数拓扑分层。它还形成了$ n $标记点的配置空间的单元格分解。此外，我们证明，由Maurer-Cartan方程统治的变形理论的经典工具只能在当地用于高斯 - 斯基兹兹。我们证明，高斯 - 斯基兹兹的变形受汉密尔顿 - 雅各比微分方程的约束。这给出了有关斋藤的Frobenius歧管的发展。最后，引入了高斯 - 史基兹（Gauss-Skizze Operad）。它是一个丰富的富尔顿 - 麦克弗森（Macpherson）的Operad，在拓扑上等同于小型2碟Operad。
The configuration space of $n$ marked points on the complex plane is considered. We investigate a decomposition of this space by so-called Gauss-skizze i.e. a class of graphs being forests, introduced by Gauss. It is proved that this decomposition is a semi-algebraic topological stratification. It also forms a cell decomposition of the configuration space of $n$ marked points. Moreover, we prove that classical tools from deformation theory, ruled by a Maurer--Cartan equation, can be used only locally for Gauss-skizze. We prove that the deformation of the Gauss-skizze is governed by a Hamilton--Jacobi differential equation. This gives developments concerning Saito's Frobenius manifold. Finally, a Gauss-skizze operad is introduced. It is an enriched Fulton--MacPherson operad, topologically equivalent to the little 2-disc operad.
