The divisor class group of splittable Zariski surfaces

Let k be an algebraically closed field of characteristic p > 0 and g is an element of k[x, y]. Let X-g subset of A(k)(3) be a normal variety defined by the equation z(p) = g(x,y). If g is a product of n linear factors in k[x,y], not necessarily homogeneous, where n equals the degree of g, we say that X-g is splittable. In this paper, we calculate the group of Weil divisors of a splittable X-g for a generic g when the characteristic of k equals 2. In the process, we describe a general approach to studying class groups of splittable X-g that we believe should yield results when p > 2.