Projectable Veronese varieties (Q2430529)

Let \(X\) be a non degenerate, reduced, reducible algebraic variety, which is embedded in an \(N\)-dimensional projective space, of pure dimension \(m\geq 3\). In this paper, the authors introduce the notion of \(x\)-projectable Veronese varieties. An \(x\)-projectable Veronese variety \(X\) means that \(N\geq m+x+1\), \(X\) is of minimal degree, connected in codimension \(1\) and isomorphically projectable into a linear space of dimension \(m+x\). The main results of this paper are the following: (1) A precise description of all \(x\)-projectable Veronese varieties having only linear components. (2) There are no \(2\)-projectable varieties with \(m\geq 3\). (3) A complete classification of \(3\)-projectable varieties. There are \(9\) types in the list.