  We establish basic techniques for studying the ideals of secant varieties of
Segre varieties. We solve a conjecture of Garcia, Stillman and Sturmfels on the
generators of the ideal of the first secant variety in the case of three
factors and solve the conjecture set-theoretically for an arbitrary number of
factors. We determine the low degree components of the ideals of secant
varieties of small dimension in a few cases.
