Fubini's theorem in codimension two

Journal Article (Journal Article)

We classify codimension two complex submanifolds of projective space X n ⊂ having the property that any line through a general point x ∈ X having contact to order two with X at x automatically has contact to order three. We give applications to the study of the Debarre-de Jong conjecture and of varieties whose Fano variety of lines has dimension 2n - 4. © Walter de Gruyter Berlin · New York 2009.