# A quintic hypersurface in P8(C) with many nodes

Oliver Schmidt, Oliver Labs, Duco van Straten

Number | 28 |
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Author | Duco van Straten |

Year | 2009 |

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