论文标题
Del Pezzo表面的同位素类别
Isotopy classes of involutions of del Pezzo surfaces
论文作者
论文摘要
令$ m_n：= \ mathbb {cp}^2 \＃n \ overline {\ mathbb {cp}^2} $对于$ 0 \ leq n \ leq 8 $是$ 9-n $ del pezzo Surface的基础光滑的平滑歧管。我们证明了有关映射类组$ \ text {mod}（m_n）的三个结果：=π_0（\ text {homeo}^+（m_n））$： 1。用于$ \ text {mod}（m_n）$的所有对象的分类和结构定理的分类和结构定理 2。对于平稳的尼尔森实现问题的积极解决方案，用于$ m_n $， 3。对某些$ m_n $的三种非凡的互动的纯粹拓扑表征来自Birational几何：deJonquiéres的互动，Geiser的互动和Bertini的参与。 一种主要成分是双曲反射组的理论。
Let $M_n := \mathbb{CP}^2 \# n\overline{\mathbb{CP}^2}$ for $0 \leq n \leq 8$ be the underlying smooth manifold of a degree $9-n$ del Pezzo surface. We prove three results about the mapping class group $\text{Mod}(M_n) := π_0(\text{Homeo}^+(M_n))$: 1. the classification of, and a structure theorem for, all involutions in $\text{Mod}(M_n)$, 2. a positive solution to the smooth Nielsen realization problem for involutions of $M_n$, and 3. a purely topological characterization of three remarkable types of involutions on certain $M_n$ coming from birational geometry: de Jonquiéres involutions, Geiser involutions, and Bertini involutions. One main ingredient is the theory of hyperbolic reflection groups.
