Bertini- type theorems in positive characteristic
Let \(k\) be an algebraically closed field, \(X\) be a scheme of finite type over the projective space of dimension \(n\) over \(k\). We prove that if \(X\) is geometrically unibranch, a general hyperplane section of \(X\) is geometrically unibranch. We also prove that if \(X\) satisfies some technical condition \((R)\) (resp. \((N))\), then a general hyperplane section of \(X\) is smooth on \(k\) (resp. normal) if \(X\) is smooth on \(k\) (resp. normal). If \(k\) is of characteristic zero or if \(X\) is unramified over the projective space, then the condition \((R)\) (resp. \((N))\) holds automatically.
scientific article; zbMATH DE number 756420