The crossing number of polynomial curve systems

TL;DR

This paper calculates the crossing number of polynomial curve systems on standard surfaces, relating it to the surface's genus with high accuracy, advancing understanding in topological graph theory.

Contribution

It provides a precise determination of crossing numbers for polynomial curve systems on surfaces, linking geometric complexity to surface genus.

Findings

Crossing number expressed in terms of surface genus

High-precision calculations achieved

Applicable to polynomial curve systems on standard surfaces

Abstract

We determine the crossing number of polynomial size curve systems on standard surfaces, in terms of the genus, up to high precision.