Semiquadratic sets and embedded polar spaces
This interesting paper is an essay on embedded polar spaces. No new results are proved, but the theory and proofs are streamlined. Moreover, the author uses some new ideas to present synthetic non-inductive arguments (and consequently no finiteness assumption is needed). The basic tool is the notion of a ``semiquadratic set'' as introduced by \textit{F. Buekenhout} and \textit{C. Lefevre} [J. Geom. 7, 17-42 (1976; Zbl 0312.50021)]. In fact, the whole paper can be seen as an application of this notion. Although this paper does not really contain new results, it contains many new ideas and I would highly recommend it as both a survey paper and a kind of demonstration paper of how beautiful and strong pure geometry can be.
scientific article; zbMATH DE number 1292222
scientific article