Automorphisms of a generic Jacobian Kummer surface (Q1302105)

Let \(C\) be a smooth curve of genus \(2\). The quotient of the Jacobian \(J(C)\), modulo the natural involution, can be embedded in \({\mathbb P}^3\) as a quartic surface \(F\) with \(16\) nodes. The desingularization of \(F\) is the Kummer surface associated with \(C\). Recently, Keum and Kondo provided a complete list of generators for the automorphism group of the Kummer surface \(X\) associated with a general curve. Looking carefully at the list, the author shows in the present paper that all the previous automorphisms of \(X\) are induced by Cremona transformations of \({\mathbb P}^3\).