# Degree of unirational parametrization of hypersurfaces

Let $X_d\subset \mathbb P^{n+1}_{\mathbb C}$ be a smooth hypersurface of ddegree $d$. Harris, Mazur and Pandharipande proved that there is a bound $b(d)$ such that if $n>b(d)$, $X_d$ is unirational. Is there a formula for the degree (in function of $d$) of the unirational parametrization one gets with their method?

• I do not remember the bound, but I remember that it is an iterated exponential in $d$. You might also look at the article by Paranjape and Srinivas, who prove roughly the same result (the basic technique goes back to Morin and Predonzan). Jul 20, 2017 at 11:41