Mathematical Research Letters

Volume 25 (2018)

Number 5

Galois descent for the gonality of curves

Pages: 1567 – 1589

DOI: https://dx.doi.org/10.4310/MRL.2018.v25.n5.a10

Authors

Joaquim Roé (Departament de Matemàtiques, Universitat Autònoma de Barcelona, Catalonia)

Xavier Xarles (Departament de Matemàtiques, Universitat Autònoma de Barcelona, Catalonia)

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.

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The authors were partially supported by the MTM 2013-40680-P and MTM 2016-75980-P (Spanish MICINN grants). The first author was supported also by the 2014 SGR 114 (Catalan AGAUR grant).

Received 5 March 2015

Accepted 28 June 2017

Published 1 February 2019