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