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

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 (d1,,dk) complete intersection in N has separable covering gonality at least d N + 1, where d = d1 + + dk. We also show that the very general such hypersurface has covering gonality at least 1 2(d N + 2).

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covering gonality, gonality, measures of irrationality, complete intersections
Mathematical Subject Classification
Primary: 14E08
Secondary: 14C15, 14M10
Received: 26 June 2020
Revised: 18 April 2021
Accepted: 4 July 2021
Published: 9 July 2022
Geoffrey Smith
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
Chicago, IL
United States