A Projective Surface of Degree Eight with 168 Nodes

TL;DR

This paper constructs a degree-eight projective surface with 168 nodes, improving the lower bound for the maximum number of ordinary double points on such surfaces.

Contribution

It provides the first explicit example of a degree-eight surface with 168 nodes, narrowing the known bounds for the maximum number of nodes.

Findings

Constructed a degree-eight surface with 168 nodes

Improved the lower bound for maximal nodes on degree-eight surfaces

Refined the estimate for the maximum number of nodes to between 168 and 174

Abstract

The estimate for the maximal number of ordinary double points of a projective surface of degree eight is improved to $168\leq\mu(8)\leq 174$ by constructing a projective surface of degree eight with 168 nodes.