2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67619For a hypersurface in complex projective space $X\subset \PP^n$, we investigate the singularities and Kodaira dimension of the Kontsevich moduli spaces $\Kbm{0,0}{X,e}$ parametrizing rational curves of degree $e$ on $X$. If $d+e \leq n$ and $X$ is a general hypersurface of degree $d$, we prove that $\Kbm{0,0}{X,e}$ has only canonical singularities and we conjecture the same is true for the coarse moduli space $\kbm{0,0}{X,e}$.This investigation is motivated by the question of which Fano hypersurfaces are unirational.56 pagesAlgebraic Geometry14C05; 14E08text