  In this short note we revisit the `shift-desingularization' version of the
$[Q,R]=0$ theorem for possibly singular symplectic quotients. We take as
starting point an elegant proof due to Szenes-Vergne of the quasi-polynomial
behavior of the multiplicity as a function of the tensor power of the
prequantum line bundle. We use the Berline-Vergne index formula and the
stationary phase expansion to compute the quasi-polynomial, adapting an early
approach of Meinrenken.
