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Working paper

Some remarks on osculating self-dual varieties

Let us say that a curve C⊂ℙ3 is osculating self-dual if it is projectively equivalent to the curve in the dual space (ℙ3)∗ whose points are osculating planes to~C. Similarly, we say that a k-dimensional subvariety X⊂ℙ2k+1 is osculating self-dual if its second osculating space at the general point is a hyperplane and X is projectively equivalent to the variety in (ℙ2k+1)∗ whose points are second osculating spaces to X. In this note we show that for each k≥1 there exist many osculating self-dual k-dimensional subvarieties in ℙ2k+1.