On the existence of a Gysin morphism for the Blow-up of an ordinary singularity

In this paper we characterize the Blowing-up maps of ordinary singularities for which there exists a natural Gysin morphism, i.e. a bivariant class $theta in Hom_{D(Y)}(Rpi_*mathbb Q_X, mathbb Q_Y)$, compatible with pullback and with restriction to the complement of the singularity.