# grobner basis of an ideal dependent on some parameter

Suppose $$I = \langle f_1, ... , f_l \rangle$$ is an ideal generated by polynomials $$f \in k[x_1,\dots,x_n]$$, where $$k$$ is a field of rational functions in some parameters $$s_1,\dots,s_m$$.

What are the techniques to study the dependence of the grobner basis of $$I$$ (with respect to some order) on the parameters $$s$$? Is it possible to find "regions" in the parameter space where the basis is doesn't change?