论文标题
丰富的结构和对数紧凑型的模量堆栈
The moduli stack of enriched structures and a logarithmic compactification
论文作者
论文摘要
Mainò（[MAI98]）和[BH19]中的一般基础方案对富集的曲线进行了研究。在本文中，我们从对数观点研究了丰富的曲线：我们对丰富的对数曲线进行简洁的定义，该曲线是对数曲线堆栈的开放式替代，并将富集的曲线定义为具有最小丰富的对数结构的曲线。这种对数观点却是一种富集结构的自然语言，自然而然地导致了一个简单的模块化紧凑型。这种模块化压实是对日志曲线堆栈的平滑日志爆炸，从[BH19]中回答了两个问题。我们还将丰富曲线的概念推广到$ r $ $ - 富含的曲线，并显示出相似的结果。我们包括一章，其中一些关键定义仅以真实的热带几何形状的语言。
Enriched curves have been studied over algebraically closed fields by Mainò ([Mai98]) and recently over general base schemes in [BH19]. In this paper, we study enriched curves from a logarithmic viewpoint: we give a succinct definition of the stack of rich log curves, which is an open substack of the stack of log curves, and define an enriched curve to be a curve with a minimal rich log structure on it. This logarithmic view point turns out to be a natural language for enriched structures, leading naturally to a simple modular compactification. This modular compactification is a smooth log blowup of the stack of log curves, answering affirmatively two questions from [BH19]. We also generalise the concept of rich curves to $r$-rich curves, and show similar results. We include a chapter phrasing some of the key definitions solely in the language of real tropical geometry.
