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

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.''

arXiv comment33 pages, expository, to appear in Springer Lecture Notes in Mathematics, comments welcome

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