Curves on complete intersections and measures of irrationality

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.

arXiv comment32 pages, with an appendix by Mohan Swaminathan. V2: Fixed typos and added a section 6