zbMATH — the first resource for mathematics

On varieties of minimal degree. (A centennial account). (English) Zbl 0646.14036
Algebraic geometry, Proc. Summer Res. Inst., Brunswick/Maine 1985, part 1, Proc. Symp. Pure Math. 46, 3-13 (1987).
[For the entire collection see Zbl 0626.00011.]
A variety \(X\subset \underset \tilde{} P^ r\) is called a “variety of minimal degreee” if it is nondegenerate (that is, it does not lie in a hyperplane) and \(\deg (X)=1+co\dim (X)\). In 1886 Del Pezzo gave a classification for surfaces of minimal degree, and in 1907 Beltrami showed how to deduce a similar classification for varieties of any dimension. The authors of the present paper give a proof of the Del Pezzo-Bertini theorem, valid in any characteristic, based on a result that makes it possible to regard any variety X of minimal degree as a divisor on a scroll, and then to use the geometry of scrolls.
Reviewer: E.J.F.Primrose

14N05 Projective techniques in algebraic geometry
14J99 Surfaces and higher-dimensional varieties
14-03 History of algebraic geometry
01A60 History of mathematics in the 20th century