Curves on complete intersections and measures of irrationality

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Abstract

We study the minimal degrees and gonalities of curves on complete intersections. We prove a classical conjecture which asserts that the degree of any curve on a general complete intersection X PN cut out by polynomials of large degrees is bounded from below by the degree of X. As an application, we verify a conjecture of Bastianelli--De Poi--Ein--Lazarsfeld--Ullery on measures of irrationality for complete intersections.

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Chen et al. (Mon,) studied this question.

synapsesocial.com/papers/68e64779b6db6435875d92a3 https://doi.org/https://doi.org/10.48550/arxiv.2406.12101

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