Enriques Surfaces and jacobian elliptic K3 surfaces

TL;DR

This paper introduces a new geometric method to construct Enriques surfaces from Jacobian elliptic K3 surfaces, revealing their automorphisms and Brauer group properties, with implications for arithmetic geometry.

Contribution

It presents a novel construction of Enriques surfaces via quadratic base change from rational elliptic surfaces, linking their elliptic fibrations and automorphisms.

Findings

Characterization of Enriques surfaces with elliptic fibrations and rational bisections

Answer to Beauville's question on exceptional Brauer group behaviour

Framework for studying automorphisms of Enriques surfaces

Abstract

This paper proposes a new geometric construction of Enriques surfaces. Its starting point are K3 surfaces with jacobian elliptic fibration which arise from rational elliptic surfaces by a quadratic base change. The Enriques surfaces obtained in this way are characterised by elliptic fibrations with a rational curve as bisection which splits into two sections on the covering K3 surface. The construction has applications to the study of Enriques surfaces with specific automorphisms. It also allows us to answer a question of Beauville about Enriques surfaces whose Brauer groups show an exceptional behaviour. In a forthcoming paper, we will study arithmetic consequences of our construction.