Covering gonalities of complete intersections in positive characteristic

Smith, Geoffrey

doi:10.2140/ant.2022.16.731

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Covering gonalities of complete intersections in positive characteristic

Geoffrey Smith

Vol. 16 (2022), No. 3, 731–745

DOI: 10.2140/ant.2022.16.731

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 $(d_{1}, \dots, d_{k})$ complete intersection in $ℙ^{N}$ has separable covering gonality at least $d - N + 1$ , where $d = d_{1} + \dots + d_{k}$ . We also show that the very general such hypersurface has covering gonality at least $\frac{1}{2} (d - N + 2)$ .

Keywords

covering gonality, gonality, measures of irrationality, complete intersections

Mathematical Subject Classification

Primary: 14E08

Secondary: 14C15, 14M10

Milestones

Received: 26 June 2020

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

Vol. 16, No. 3, 2022