The divisor class group of splittable Zariski surfaces

Abstract

Let [Formula: see text] be an algebraically closed field of characteristic [Formula: see text] and [Formula: see text]. Let [Formula: see text] be a normal variety defined by the equation [Formula: see text]. If [Formula: see text] is a product of [Formula: see text] linear factors in [Formula: see text], not necessarily homogeneous, where [Formula: see text] equals the degree of [Formula: see text], we say that [Formula: see text] is splittable. In this paper, we calculate the group of Weil divisors of a splittable [Formula: see text] for a generic [Formula: see text] when the characteristic of [Formula: see text] equals [Formula: see text]. In the process, we describe a general approach to studying class groups of splittable [Formula: see text] that we believe should yield results when [Formula: see text].