  In this paper, we survey the theory of Cartwright-Sturmfels ideals. These are
Z^n-graded ideals, whose multigraded generic initial ideal is radical.
Cartwright-Sturmfels ideals have surprising properties, mostly stemming from
the fact that their Hilbert scheme only contains one Borel-fixed point. This
has consequences, e.g., on their universal Groebner bases and on the family of
their initial ideals. In this paper, we discuss several known classes of
Cartwright-Sturmfels ideals and we find a new one. Among determinantal ideals
of same-size minors of a matrix of variables and Schubert determinantal ideals,
we are able to characterize those that are Cartwright-Sturmfels.
