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1College Station. e-mail: jml@math.tamu.edu
2College Station. e-mail: robles@math.tamu.edu
Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2009, Issue 631, Pages 221–235, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2009.047, March 2009
We classify codimension two complex submanifolds of projective space Xn ⊂ 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.
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