The 1959 annali di matematica paper of Beniamino Segre and its legacy
For the development of finite geometries two of the most influential papers have been ``Le geometrie di Galois'' [Ann. Mat. Pura Appl., IV. Ser. 48, 1-96 (1959; Zbl 0093.33604)] and ``Ovals in a finite projective plane'' [Can. J. Math. 7, 414-416 (1955; Zbl 0065.13402)], both by \textit{B. Segre}. In the paper of 1959 he developed the theoretical foundations of characterizing algebraic varieties by combinatorial properties. The result of the paper of 1955 states that for \(q\) odd, a set of \(q + 1\) points such that no three of them are collinear, is the set of rational points of a conic. This result has been a sort of blueprint for much further research. The article of Hirschfeld under review summarizes the results of the fundamental paper of 1959 and provides an overview about further research of Segre as well as of other researchers.
scientific article; zbMATH DE number 1972485