标题： 具有碰撞点的曲线：对数和堆叠 显示英文标题

标题： Curves with colliding points: logarithmic and stacky

摘要： 我们引入了一种广义对数扭转曲线的新概念，这些曲线是在带标记的节点曲线上在标记点处附加额外数据的曲线。当标记互不相同时，这一概念与阿布拉莫维奇和维斯托利引入的扭转曲线的概念一致。除了发展基本概念和结果外，本文还研究了这类曲线的模空间以及它们之间的收缩映射。部分动机来自对扭转稳定映射的应用，这将在后续文章中研究。 显示英文摘要

摘要： We introduce a new notion of generalized log twisted curves, which are marked nodal curves with additional data at the marked points. In the case when the markings are distinct this notion agrees with the notion of twisted curve introduced by Abramovich and Vistoli. In addition to developing the basic notions and results, we study in this article the moduli of such curves as well as contraction maps between them. This is motivated, in part, by applications to twisted stable maps which will be studied in a subsequent article.