#### Vol. 16, No. 3, 2022

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Covering gonalities of complete intersections in positive characteristic

### Geoffrey Smith

Vol. 16 (2022), No. 3, 731–745
##### Abstract

We define the covering gonality and separable covering gonality of varieties over arbitrary fields, generalizing the definition given by Bastianelli, De Poi, Ein, Lazarsfeld, and Ullery for complex varieties. We show that, over an algebraically closed field, a smooth multidegree $\left({d}_{1},\dots ,{d}_{k}\right)$ complete intersection in ${ℙ}^{N}$ has separable covering gonality at least $d-N+1$, where $d={d}_{1}+\cdots +{d}_{k}$. We also show that the very general such hypersurface has covering gonality at least $\frac{1}{2}\left(d-N+2\right)$.

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##### Keywords
covering gonality, gonality, measures of irrationality, complete intersections
##### Mathematical Subject Classification
Primary: 14E08
Secondary: 14C15, 14M10
##### Milestones
Revised: 18 April 2021
Accepted: 4 July 2021
Published: 9 July 2022
##### Authors
 Geoffrey Smith Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago Chicago, IL United States