The rationality of the moduli spaces of trigonal curves of odd genus

TL;DR

This paper proves that the moduli spaces of trigonal curves of odd genus greater than 4 are rational, establishing their geometric simplicity and structure.

Contribution

It demonstrates the rationality of moduli spaces for trigonal curves of odd genus greater than 4, a significant advancement in algebraic geometry.

Findings

Moduli spaces of trigonal curves of odd genus > 4 are rational.

The rationality result applies to all odd genus g > 4.

This contributes to understanding the geometry of algebraic curves.

Abstract

The moduli spaces of trigonal curves of odd genus $g>4$ are proven to be rational.