Kummer's quartics and numerically reflective involutions of Enriques surfaces (Q763984)

The present paper goes a step further in the classification of involutions on Enriques surfaces, analyzing the case of numerically reflexive involutions. An involution \(\sigma\) of an Enriques surface \(S\) is said to be \textit{numerically reflexive} if it acts as a reflection on the cohomology group \(H^2(S,\mathbb{Q})\). The author shows that numerically reflexive involution act on the second cohomology in two different ways, one of which can be explicitly constructed using the Jacobian \(J(C)\) of a genus two curve \(C\) and a particular subgroup of its involutions, called Göpel subgroup. The author also gives a deep analysis of an example of \textit{J. I. Hutchinson} [American M. S. Bull. (2) 7, 211--217 (1901; JFM 32.0641.09)] regarding an involution obtained via an elementary Cremona transformation of the quotient Kummer surface \(J(C)/\{\pm 1\}\subset\mathbb{P}^3\), which he uses to prove his main result.