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

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

2009-09-18

arxiv.org/abs/0909.3367v1

Mathematics

Algebraic Geometry

21 pages, 1 figure

Scientific paper

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 $\mu_{8}(5)$ of ordinary nodes a hyperquintic in $\PP^8(\CC)$ can have to $23436 \leq \mu_{8}(5) \leq 27876$. 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.

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