A primer on measures of irrationality
Algebraic Geometry
2025-09-05 v1
Abstract
Measures of irrationality are a numerical way of quantifying how far a given variety is from being rational (or rationally connected, uniruled, etc.). In the last two decades, there has been renewed interest in the study of these invariants. The goal of this expository survey is to summarize known results from the point of view of the Kodaira--Enriques classification of surfaces, highlight recent progress, and discuss a number of open problems and questions.
Keywords
Cite
@article{arxiv.2509.03783,
title = {A primer on measures of irrationality},
author = {Nathan Chen and Olivier Martin},
journal= {arXiv preprint arXiv:2509.03783},
year = {2025}
}
Comments
29 pages; this work grew out of the March 2024 AIM workshop "Degree d points on algebraic surfaces"