Rationality of some tetragonal loci

TL;DR

This paper proves the rationality of the moduli space of tetragonal curves for specific genera based on their congruence classes modulo 12, expanding understanding of the geometric properties of these moduli spaces.

Contribution

It establishes the rationality of the moduli space of tetragonal curves for an infinite set of genera defined by certain congruence conditions, with specific exceptions.

Findings

Moduli space of tetragonal curves is rational for g ≡ 1, 2, 5, 6, 9, 10 (mod 12)

Rationality holds for all g in these classes except g=9, 45

Provides new insights into the structure of tetragonal loci in algebraic geometry.

Abstract

We prove that the moduli space of tetragonal curves of genus g>6 is rational when g is congruent to 1, 2, 5, 6, 9, 10 modulo 12 and not equal to 9, 45.