A Generalization of the Dual Kummer Surface

Abstract

Given a hyperelliptic curve \({\mathcal{C}}\) of genus g, we construct a variety \({\mathcal{k}}^*\) with a hyperplane section Hm whose complement \({\mathcal{k}}^*_m\) parametrizes classes of divisors on \({\mathcal{C}}\) of degree g + 1, in general position, modulo the ± Y involution. The variety \({\mathcal{k}}^*\) is birational to the Kummer variety belonging to \({\mathcal{C}}\). It is a tool for studying rational classes and divisors. The variety \({\mathcal{k}}^*_m\) is birational to a quotient of an affine variety by an affine group.