Spaces of rational curves on hypersurfaces (Q2870990)

This is a review of the space of rational curves on hypersurfaces, focusing on the recent results obtained by the authors. Section 2 contains some results (both classical and relatively new) about lines on hypersurfaces. These results are also used for induction in their prove of irreduciblity (following Harris-Roth-Starr [\textit{J. Harris} et al., J. Reine Angew. Math. 571, 73--106 (2004; Zbl 1052.14027)]). Section 3 introduces the Kontsevich space of stable maps. Section 4 and 5 study conics in hypersurfaces, which is a crucial part of their proof.