Fubini's theorem in codimension two
Copyright policy )Fubini's theorem in codimension two
We classify codimension two analytic submanifolds X of projective space having the property that any line through a general point p having contact to order two with X at p automatically has contact to order three. We give applications to the study of the Debarre--de Jong conjecture, and of n-dimensional varieties whose Fano variety of lines has dimension 2n-4.
v.1, 11 pages
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Mathematics - Differential Geometry, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), FOS: Mathematics, 53A20, 14N15; 51N15; 53A20, 51N15, Algebraic Geometry (math.AG), 14N15
Mathematics - Differential Geometry, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), FOS: Mathematics, 53A20, 14N15; 51N15; 53A20, 51N15, Algebraic Geometry (math.AG), 14N15
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