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

Oliver Schmidt; Oliver Labs; Duco van Straten

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

Algebraic Geometry 2009-09-21 v1

Authors: Oliver Schmidt , Oliver Labs , Duco van Straten

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 $\mu_{8}(5)$ 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.

Keywords

quintic hypersurface ordinary nodes projective space singularities maximum number of nodes

Cite

@article{arxiv.0909.3367,
  title  = {A Quintic Hypersurface in $\PP^8(\CC)$ with Many Nodes},
  author = {Oliver Schmidt and Oliver Labs and Duco van Straten},
  journal= {arXiv preprint arXiv:0909.3367},
  year   = {2009}
}

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21 pages, 1 figure

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

Abstract

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