Rational curves on low degree hypersurfaces
-- Jason Starr, March 26, 2004

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This talk will describe what is and is not known about
spaces of rational curves on low degree hypersurfaces: irreducibility,
dimension, singularities and Kodaira dimension.


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There are 2 goals behind these questions (neither finished).  The first is
to extend the Tsen-Lang theorem about rational points on hypersurfaces
defined over the function field of a surface.  The second is to prove
there exists a smooth Fano hypersurface that is not uniruled.

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This is joint work with Johan de Jong, Joe Harris and Mike Roth.