REVIEW 1 cited by
A Septic with 99 real Nodes
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
We find a surface of degree 7 in real projective three-space P^3(R) with 99 real nodes within a family of surfaces with dihedral symmetry: First, we consider this family over some small prime fields, which allows us to test all possible parameter sets using computer algebra. In this way we find some examples of 99-nodal surfaces over some of these finite fields. Then, the examination of the geometry of these surfaces allows us to determine the parameters of a 99-nodal septic in characteristic zero. This narrows the possibilities for \mu(7), the maximum number of nodes on a septic, to: 99 <= \mu(7) <= 104. When reducing our surface modulo 5, we even obtain a 100-nodal septic in P^3(F_5).
Forward citations
Cited by 1 Pith paper
-
Nodal surfaces in $\mathbb{P}^3$ and coding theory
The binary linear code associated to any sextic surface in P^3 with 65 nodes is unique: it is the [65,12,{24,32,40}] code of the Barth sextic.
Discussion (0). Continue with ORCID to comment.