THE BKK ROOT COUNT IN C-N

The root count developed by Bernshtein, Kushnirenko and Khovanskii onl y counts the number of isolated zeros of a polynomial system in the al gebraic torus (C)(n). In this paper, we modify this bound slightly so that it counts the number of isolated zeros in C-n. Our bound is, app arently, significantly sharper than the recent root counts found by Ro jas and in many cases easier to compute. As a consequence of our resul t, the Huber-Sturmfels homotopy for finding all the isolated zeros of a polynomial system in (C)(n) can be slightly modified to obtain all the isolated zeros in C-n.