Enriques Surfaces - Brauer groups and Kummer structures

TL;DR

This paper constructs families of complex Enriques surfaces with trivial Brauer groups upon pullback to their K3 covers, using isogenies with Kummer surfaces and exploring connections to string theory and Calabi-Yau threefolds.

Contribution

It introduces new lattice theoretic and geometric methods to produce Enriques surfaces with specific Brauer group properties, linking algebraic geometry to string theory.

Findings

Families of Enriques surfaces with zero Brauer group pullback

Use of isogenies with Kummer surfaces of product type

Connections to string theory and Calabi-Yau threefolds

Abstract

This paper develops families of complex Enriques surfaces whose Brauer groups pull back identically to zero on the covering K3 surfaces. Our methods rely on isogenies with Kummer surfaces of product type. We offer both lattice theoretic and geometric constructions. We also sketch how the construction connects to string theory and Picard-Fuchs equations in the context of Enriques Calabi-Yau threefolds.