Gauss Maps, Tangential and Dual Varieties

Abstract

In the preceding lecture, we associated to each point of a projective variety X ⊂ ℙⁿ a linear subspace of ℙ ⁿ. We investigate here how those planes vary on X, that is, the geometry of the Gauss map. Before we launch into this, however, we should take a moment to discuss a question that will be increasingly relevant to our analysis; the choice of our ground field K and in particular its characteristic.