三角形相似类的叠

Eric Brussel; Madeleine Goertz; Elijah Guptill; Kelly Lyle

三角形相似类的叠

代数几何 2025-08-01 v3 动力系统

作者: Eric Brussel , Madeleine Goertz , Elijah Guptill , Kelly Lyle

摘要

我们构造了带标签、有向三角形相似类的光滑紧模空间。该空间记为 $\mathfrak D$ ，是三个射影平面的连通和，并通过爆破投影到文献中出现的两个形状空间：著名的（Riemann）球面（\cite{Kend84}, \cite{Beh}, \cite{Montgomery}, \cite{ES15}）以及较不为人知的2-环面（\cite{BG23}）。二面体群 $D_6$ 的自然作用定义了绝对（无标签、无向）类的商叠 $[\mathfrak D/D_6]$ 。

关键词

模空间相似类三角形商叠二面体群旗流形形状空间爆破投影

引用

@article{arxiv.2408.07792,
  title  = {The Stack of Similarity Classes of Triangles},
  author = {Eric Brussel and Madeleine Goertz and Elijah Guptill and Kelly Lyle},
  journal= {arXiv preprint arXiv:2408.07792},
  year   = {2025}
}

备注

26 pages. Changes primarily include increased detail, more pictures, and better exposition. Semple and Fulton-MacPherson are more fully integrated. The order of sections is changed, some new ones added, some old ones deleted. No main results are added, and none removed

三角形相似类的叠

摘要

关键词

引用

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