Rational curves on hypersurfaces
-- Eric Riedl, October 10, 2014

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Let X be a general degree d hypersurface in n-dimensional
projective space, and consider the spaces of rational curves on
X. Joint with David Yang, following work of Harris, Roth,
Starr, Beheshti and Kumar, we prove that the space of degree e
rational curves on X is irreducible and we compute its
dimension for n > d+1.  This resolves all but the n = d+1 case
of a conjecture of Coskun, Harris and Starr.