Space of initial conditions for the four-dimensional Fuji-Suzuki-Tsuda system (Mathematical structures of integrable systems, its deepening and expansion)

Abstract

A geometric study for an integrable 4-dimensional dynamical system so called the Fuji-Suzuki-Tsuda system is given. By the resolution of indeterminacy, the group of its Bäklund transformations is lifted to a group of pseudo-isomorphisms between rational varieties obtained from (P¹)⁴ by blowing-up along eight 2-dimensional subvarieties and four 1-dimensional sub-varieties. The root basis is realised in the Néron-Severi bilattices. A discrete Painlevé system with quadratic degree growth is also realised as its translational element.