A class of geometrically elliptic fibrations by plane projective quartic curves

2025/10/28 by Hilario, Cesar, Stöhr, Karl Otto
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.24862

Abstract

We investigate fibrations by non-hyperelliptic curves of arithmetic genus three and geometric genus one in characteristic two. Assuming that there is only one moving singularity and that its image in the Frobenius pullback of the fibration has degree one over the base, we provide a complete classification up to birational equivalence. This relies on an in-depth analysis of the generic fibres, whose geometry we describe explicitly. We prove that these fibrations are covered by elliptic fibrations, and that the covers are birational on the fibres but purely inseparable of exponent one on the bases.

Citations

• Non-smooth regular curves via a descent approach
• Fibrations by plane projective rational quartic curves in characteristic two
• On genus-change in algebraic curves over nonperfect fields

Related

• Fibrations by plane quartic curves with a canonical moving singularity
• Fibrations by plane projective rational quartic curves in characteristic two
• On the classification of fibrations by genus two singular curves via fibrations by elliptic curves on surfaces
• Special elliptic fibrations
• Genus 1 fibrations on the supersingular K3 surface in characteristic 2 with Artin invariant 1