Enriques surfaces covered by Jacobian Kummer surfaces

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 $\operatorname{Aut}(X)$ is generated by elements of order 2, which is an improvement of the theorem of S. Kondo.