An algebraic proof of Zak's inequality for the dimension of the Gauss image (Q1566430)

Let \(X \subset \mathbb P^r\) be an integral variety. An important theorem of Zak says that the image of the Gauss mapping of \(X\) has dimension at least \(\dim (X)-\dim (\text{Sing}(X))+1\). Here the authors give a very general proof of this result and of several generalizations of it in the set-up of commutative algebra, giving a new bound on the analytic spread of a module of Kähler differentials.