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Oberseminar SoSe 2008 Abstract to the talk by O. Tommasi

On hypersurfaces with too many lines

The study of rational curves on algebraic varieties is an important area of research in algebraic geometry. In this talk we will concentrate on a specific problem: What is the maximal dimension for a family of lines lying on a nonsingular hypersurface X of given degree in projective space?
In this talk, we will present the conjectures on this subject formulated by Debarre–De Jong and Beheshti–Starr, and outline a construction that gives a geometric explanation of why these conjectures should be true. This is joint work (in progress) with J. M. Landsberg, Texas A&M University.