“…While algebraic varieties do have some structure which can be exploited (for instance, their intersections with other algebraic sets have a bounded number of connected 5 Our argument follows the iteration ideas of Christ [6] (which in turn were inspired by the work of Bourgain, Wolff, and Schlag on Kakeya-type problems) adapted to the general vector field setting. Of course, the idea of iterating an operator supported mostly on one-dimensional sets to increase the dimension of the support is hardly new (see, e.g., [4], [9], [5], [12]); our main innovation is the utilization of the concept of width introduced in the previous section.…”