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<p>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.</p>

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A Primer on Measures of Irrationality

  • 期刊论文

  • 发表日期：

    2026年3月11日

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  • Nathan Chen,
  • Olivier Martin

摘要

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.