Partial and semipartial geometries: An update (Q1394811)

A partial linear space with \(s+1\) points per line and \(t+1\) lines per point is called an \((\alpha,\beta)\)-geometry if for \(p \notin L\) either \(\alpha\) or \(\beta\) lines through \(p\) intersect the line \(L\) [see \textit{F. De Clerck} and \textit{H. Van Maldeghem}, Chap. 12 in: Handbook of incidence geometry (ed. F. Buekenhout), North-Holland (1995; Zbl 0821.00012), for a survey of such geometries]. In the paper under review, the author reports on recent developments and new constructions of \((\alpha,\beta)\)-geometries for \(\alpha=\beta\) and for \(\beta=0\). He also provides a complete list of the parameters of all examples known so far.