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.''

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

References in corpus (2)

• The open Gromov-Witten-Welschinger theory of blowups of the projective plane
• An introduction to Bousfield localization