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

Oliver Schmidt; Oliver Labs; Duco van Straten

paper

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

arXiv:0909.3367

Abstract

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

21 pages, 1 figure