On the Debarre-de Jong and Beheshti-Starr conjectures on hypersurfaces with too many lines. Michigan Math. J. 59 (2010), no. 3, 573–588.1945-2365 The authors consider a hypersurface X n−1 ⊂ P n of degree d ≥ n. They investigate the singularities of this hypersurface by the use of the Fano scheme F(X) of lines on X and its irreducible component B ⊂ F(X) of dimension at least n − 2
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