A special configuration of 12 conics and generalized Kummer surfaces

generalized Kummer surface X obtained as the quotient of an abelian surface by a symplectic automorphism of order 3 contains a 9𝐀_2 -configuration of (-2) -curves. Such a configuration plays the role of the 16𝐀_1 -configurations for usual Kummer surfaces. In this paper we construct 9 other such 9𝐀_2 -configurations on the generalized Kummer surface associated to the double cover of the plane branched over the sextic dual curve of a cubic curve. The new 9𝐀_2 -configurations are obtained by taking the pullback of a certain configuration of 12 conics which are in special position with respect to the branch curve, plus some singular quartic curves. We then construct some automorphisms of the K3 surface sending one configuration to another. We also give various models of X and of the generic fiber of its natural elliptic pencil.