Shioda, Tetsuji On the Picard number of a Fermat surface. (English) Zbl 0567.14021 J. Fac. Sci., Univ. Tokyo, Sect. I A 28, 725-734 (1981). A general algorithm is considered for the computation of the Picard number of the Fermat surface \(X^ 2_ m=\{x^ m_ 0+x_ 1^ m+x_ 2^ m+x_ 3^ m=0\}.\) If m is not prime to 2 and 3 then the Picard number is \(\rho (X^ 2_ m)=3(m-1)(m-2)+1;\) moreover, \(NS(X^ 2_ m)\otimes {\mathbb{Q}}\) is generated by classes of straight lines on \(X^ 2_ m\). The values \(\rho (X^ 2_ m)\) have been computed also for \(m=2^ n\) and \(m=3^ n\). At the end of the article it is noted that Aoki has recently obtained a general formula for \(\rho (D^ 2_ m)\) [cf. N. Aoki, Math. Ann. 266, 23-54 (1983; Zbl 0506.14030) and ibid. 267, 572 (1984; Zbl 0534.14021)]. Cited in 5 ReviewsCited in 15 Documents MSC: 14C22 Picard groups 14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties 14J25 Special surfaces Keywords:Picard number of the Fermat surface Citations:Zbl 0516.14028; Zbl 0506.14030; Zbl 0534.14021 PDFBibTeX XMLCite \textit{T. Shioda}, J. Fac. Sci., Univ. Tokyo, Sect. I A 28, 725--734 (1981; Zbl 0567.14021)