Divisors of expected Jacobian type

Divisors whose Jacobian ideal is of linear type have received a lot attention recently because its connections with the theory $D$-modules. In this work we are interested on divisors expected type, that is, gradient and relation coincides reduction number respect to plus one. We provide conditions in order be able describe precisely equations Rees algebra ideal. also relate some $D$-module theoretic invariant given by degree Kashiwara operator.