Varieties with non-linear Gauss fibers
Let \(X \subset \mathbb P^n\) be an integral variety. In characteristic zero the general fiber of the Gauss map \(\gamma _X\) of \(X\) is a linear space, but in positive characteristic this is in general false [see \textit{A. Noma}, J. Pure Appl. Algebra 156, No. 1, 81--93 (2001; Zbl 0974.14037) and references therein]. In the paper under review for any positive characteristic algebraically closed field and for all integers \(k \geq 2\), \(0 \leq r \leq k\) and \(n \geq r+k\) and any integral \(r\)-codimensional projective variety \(Y \subseteq \mathbb P^r\) the author constructs a \(k\)-dimensional projective variety \(X \subset \mathbb P^n\) such that \(Y\) is (set-theoretically) a general fiber of \(\gamma _X\).
scientific article; zbMATH DE number 5013660
scientific article