  In this note, we show that the free generators of the Mishchenko-Fomenko
subalgebra of a complex reductive Lie algebra, constructed by the argument
shift method at a regular element, form a regular sequence. This result was
proven by Serge Ovsienko in the type A at a regular and semisimple element. Our
approach is very different, and is strongly based on geometric properties of
the nilpotent bicone.
