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arXiv · 2007.09742

An Introduction to $\mathbf{A}^1$-Enumerative Geometry

Thomas Brazelton
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Abstract

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.''

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Thomas Brazelton. 2020-07-19. An Introduction to $\mathbf{A}^1$-Enumerative Geometry. https://arxiv.org/abs/2007.09742

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