Enriques surfaces covered by Jacobian Kummer surfaces

TL;DR

This paper classifies specific Enriques surfaces covered by Jacobian Kummer surfaces, explicitly describes their involutions, and shows their automorphism groups are generated by involutions, refining previous results.

Contribution

It provides a complete classification of Enriques surfaces with a Jacobian Kummer cover and explicitly describes their involutions, advancing understanding of their automorphism groups.

Findings

Exactly 31 such Enriques surfaces exist.

Explicit description of free involutions for these surfaces.

Automorphism group generated by involutions, improving Kondo's theorem.

Abstract

This paper classifies Enriques surfaces whose K3-cover is a fixed Picard-general Jacobian Kummer surface. There are exactly 31 such surfaces. We describe the free involutions which give these Enriques surfaces explicitly. As a biproduct, we show that Aut(X) is generated by elements of order 2, which is an improvement of the theorem of S. Kondo.