Kleiman, Steven L. Bertini and his two fundamental theorems. (English) Zbl 0926.14001 Bottazzini, U. (ed.), Studies in the history of modern mathematics. III. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 55, 9-37 (1998). In the first part of the paper the author reviews Bertini’s life story. In the last part he discusses the well known fundamental theorems of Bertini on smoothness and reducible linear systems in algebraic geometry. The main ideas of the original proofs of Bertini, Enriques, Severi, Zariski, Van der Waerden and others are given. The author also proves a new extension of Bertini’s first theorem concerning the “variable \(r\)-fold points” for any \(r\).For the entire collection see [Zbl 0904.00011]. Reviewer: Lucien Bădescu (Bucureşti) Cited in 26 Documents MSC: 14-03 History of algebraic geometry 01A55 History of mathematics in the 19th century 01A60 History of mathematics in the 20th century 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry Keywords:hyperplane sections; smoothness; irreducibility; Bertini theorems; reducible linear systems PDFBibTeX XMLCite \textit{S. L. Kleiman}, in: Studies in the history of modern mathematics. III. Palermo: Circolo Matematico di Palermo. 9--37 (1998; Zbl 0926.14001) Full Text: arXiv