On the \(K\)-theory of affine hyperplanes through a linear subvariety of codimension one (Q1864692)

Let \(R\) be the coordinate ring of a union of \(n\) hyperplanes in an affine \(m\)-space over an algebraically closed field \(k\). The author calculates the Picard group in the case that the planes all contain the same linear subvariety of codimension one, and \(K_0\) in the case that the planes are all through a line in affine 3-space and \(k\) is of characteristic zero. These results extend the work of \textit{B. H. Dayton} [J. Algebra 88, 534--569 (1984; Zbl 0537.13010)] about planes through the origin, \textit{B. H. Dayton} and \textit{C. A. Weibel} [Trans. Am. Math. Soc. 257, 119--141 (1980; Zbl 0424.18011)] about planes satisfying a general position condition and \textit{F. Orecchia} [J. Pure Appl. Algebra 142, No. 1, 49--61 (1999; Zbl 0942.14025)] about lines through a point.