A Quintic Hypersurface in ${\text{PP}}^8(\text{CC})$ with Many Nodes

We construct a hypersurface of degree 5 in projective space ${\text{PP}}^8(\text{CC})$ which contains exactly 23436 ordinary nodes and no further singularities. This limits the maximum number ${\mu }_8(5)$ of ordinary nodes a hyperquintic in ${\text{PP}}^8(\text{CC})$ can have to $23436\le {\mu }_8(5)\le 27876$. Our method generalizes the approach by the $3^{\text{rd}}$ author for the construction of a quintic threefold with 130 nodes in an earlier paper.