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Curves on complete intersections and measures of irrationality

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arxiv 2406.12101 v2 pith:FXGFVYNF submitted 2024-06-17 math.AG

Nathan Chen , Benjamin Church , Junyan Zhao This is my paper
classification math.AG
keywords completeintersectionscurvesdegreeirrationalitymeasuresanswerapplication
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abstract

We study the minimal degrees and gonalities of curves on complete intersections. We prove that the degree of any curve on a general complete intersection $X \subseteq \mathbb{P}^N$ of large multidegree is bounded from below by the degree of $X$. As an application, we answer a problem of Bastianelli--De Poi--Ein--Lazarsfeld--Ullery on measures of irrationality for complete intersections.

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  1. A primer on measures of irrationality

    math.AG 2025-09 conditional

    An expository survey of degree of irrationality, covering gonality, and related invariants, organized by the Kodaira-Enriques classification, with many open problems.

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