Groupe de Picard des surfaces de Zariski. (Picard group of Zariski surfaces). (French) Zbl 0573.14012

Let k be an algebraically closed field of characteristic \(p\geq 5\). Let X, Y, Z and \(T_{ij}\) for \(0\leq i+j\leq p\) be algebraically independent variables. Let L be an algebraic closure of the field \(k(\{T_{ij}\})\). The author proves that the coordinate ring of the generic Zariski surface \(R:=L[X,Y,Z]/(Z^ p-\sum_{0\leq i+j\leq p}T_{ij}X^ iY^ j)\) is factorial.
Reviewer: R.Fossum


14C22 Picard groups
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
14J25 Special surfaces