A method for computing the kernel of a map of divisor classes of local rings in characteristic p\(\neq 0\)
Let k be an algebraically closed field of characteristic \(p=0\) and \(G\in k[X,Y]\) be an polynomial, m a natural number and \(X_ m\) the surface in \({\mathbb{A}}\) \(3_ k\) defined by \(z^{p\quad m}-G=0\). The purpose of this paper is to study the divisor class group \(Cl(X_ m)\) of \(X_ m\). The idea is to define a morphisms \(\phi_ m:\quad C1(X_{m+1})\to C1(X_ m)\) and obtain information on \(C1(X_{m+1})\) from \(C1(X_ m)\). You can find some explicit examples. It should be said that \textit{P. Samuel} calculated some examples in his book ``Lectures on unique factorization domains'' (Tata Inst. Fund. Res., Bombay 1964; Zbl 0184.066)].
scientific article; zbMATH DE number 4069049