| Résume | A classical result of Morin from 1942 shows that a general hypersurface in projective space is unirational once its degree is much smaller than its dimension; the construction is an inductive one based on fibering a hypersurface into lower degree ones via projection from a large linear space. In this talk, I will describe a new unirationality construction which based on taking residual points of highly tangent lines. This parameterization shows that a degree d hypersurface in projective n-space is unirational as soon as n ≥ 2^{d.2^d}, which significantly improves upon the previously best known bound n ≥ 2^{d!}. |
