Galois descent for the gonality of curves

TL;DR

This paper investigates how the gonality of algebraic curves behaves under base field extensions, using Galois descent techniques for morphisms to Brauer-Severi varieties and rational normal scrolls.

Contribution

It provides new conditions for the invariance of gonality under base extension and extends Galois descent theory to morphisms to Brauer-Severi varieties and rational normal scrolls.

Findings

Established criteria for gonality invariance under base change

Extended Galois descent to morphisms into Brauer-Severi varieties

Analyzed Galois descent for rational normal scrolls

Abstract

We determine conditions for the invariance of the gonality under base extension, depending on the numeric invariants of the curve. More generally, we study the Galois descent of morphisms of curves to Brauer-Severi varieties, and also of rational normal scrolls.