Splittable Zariski surfaces II

Let k be an algebraically closed field of characteristic p > 0 and . Let be the variety defined by the equation . If g is a product of n linear factors in , not necessarily homogeneous, where n equals the degree of g, we say that X-g is splittable. In this article, we calculate the group of Weil divisors of a splittable X-g for a generic g when the characteristic of k is greater than 2. We then use this calculation to determine the group of Weil divisors of generic splittable Zariski hypersurfaces in all characteristics greater than 2.