Tritangents to smooth sextic curves

TL;DR

This paper establishes upper bounds on the number of tritangents to smooth sextic curves over complex and real fields, providing new insights into their geometric properties.

Contribution

It proves that a smooth complex sextic has at most 72 tritangents, and a real sextic has at most 66 real tritangents, improving understanding of sextic curve geometry.

Findings

Maximum of 72 tritangents for complex sextics

Maximum of 66 real tritangents for real sextics

Enhanced bounds on sextic curve tangencies

Abstract

We prove that a smooth plane sextic curve can have at most 72 tritangents, whereas a smooth real sextic may have at most 66 real tritangents.