Maxim Arap

Rational curves on hypersurfaces of low degree

Abstract. The goal of this seminar is to present an outline of the proof of the following result obtained by Harris, Roth and Starr (published in 2004). If n> 2 and d < (n+1)/2 then for a general hypersurface X of degree d in P^n and for any fixed positive integer e the moduli space of rational curves of degree e on X is an integral local complete intersection of the expected dimension (n+1-d)e+n-4.