English

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

Algebraic Geometry 2020-07-21 v1 Algebraic Topology

Abstract

We provide an expository introduction to A1\mathbb{A}^1-enumerative geometry, which uses the machinery of A1\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, A1\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.''

Keywords

Cite

@article{arxiv.2007.09742,
  title  = {An Introduction to $\mathbf{A}^1$-Enumerative Geometry},
  author = {Thomas Brazelton},
  journal= {arXiv preprint arXiv:2007.09742},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-23T17:13:49.422Z