Kummer's quartic surface associated to the Clebsch top (Symmetry and Singularity of Geometric Structures and Differential Equations)

Abstract

This note deals with the Kummer surface associated to the Clebsch top with Weber's condition. The Clebsch top is an integrable system describing the rotational motion of a rigid body in an ideal fluid, under special conditions. When restricted to a specific symplectic leaf, given through the so-called Weber condition, there is an associated Kummer surface given as a quartic algebraic surface in CP3 with 16 double points. The explicit conditions of these singular points are given by theoretical computations and are verified by numerical computation through Grabner bases.