We show that the Kontsevich space of rational curves of degree at most roughly on a general hypersurface of degree is equidimensional of expected dimension and has two components: one consisting generically of smooth embedded rational curves and the other consisting of multiple covers of a line. This proves more cases of a conjecture of Coskun, Harris, and Starr and shows that the Gromov–Witten invariants in these cases are enumerative.
"A Note on Rational Curves on General Fano Hypersurfaces." Michigan Math. J. 68 (4) 755 - 774, November 2019. https://doi.org/10.1307/mmj/1567735281