Varieties with many lines
Let \(X\) be a \(k\)-dimensional irreducible algebraic subvariety of the \(n\)- dimensional complex projective space \(\mathbb{P}^ n\). The author proves that if \(X\) has codimension bigger than two and contains a \((2k - 4)\)- dimensional family of lines, then \(X\) is either a one-dimensional family of quadrics, or a two-dimensional family of \((k-2)\)-dimensional projective spaces, or a linear section of the Grassmann variety of lines of \(\mathbb{P}^ 4\).
scientific article; zbMATH DE number 599659