Rational curves on hypersurfaces of low degree, II

Mathematics – Algebraic Geometry

Scientific paper

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47 pages

Scientific paper

This is a continuation of "Rational curves on hypersurfaces of low degree",
math.AG/0203088. We prove that if d^2+d+1 < n and d > 2, then for a general
hypersurface X_d in P^n of degree d, for each degree e the space of rational
curves of degree e on X is itself a rationally connected variety.

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