论文标题
$ \ Mathbf {a}^1 $ - 增强几何形状的简介
An Introduction to $\mathbf{A}^1$-Enumerative Geometry
论文作者
论文摘要
我们提供了$ \ mathbb {a}^1 $元素几何形状的说明性介绍，该几何形状使用$ \ mathbb {a}^1 $ -Homotopy理论的机械来丰富经典的经典枚举几何学在更广泛的字段上质疑。其中包括对平滑方案的丰富局部形态的讨论，跟随莫雷尔，$ \ mathbb {a}^1 $ -Milnor数字，以及各种计算工具和最新示例。 基于Kirsten Wickelgren在2018年LMS-CMI暑期学校发表的演讲，“同型理论和算术几何，动机和毒液剂方面。”
We provide an expository introduction to $\mathbb{A}^1$-enumerative geometry, which uses the machinery of $\mathbb{A}^1$-homotopy theory to enrich classical enumerative geometry questions over a broader range of fields. Included is a discussion of enriched local degrees of morphisms of smooth schemes, following Morel, $\mathbb{A}^1$-Milnor numbers, as well as various computational tools and recent examples. Based off lectures delivered by Kirsten Wickelgren at the 2018 LMS-CMI summer school ''Homotopy Theory and Arithmetic Geometry, Motivic and Diophantine Aspects.''
