Rationality of moduli spaces of plane curves of small degree

TL;DR

This paper investigates the rationality of moduli spaces of plane curves of small degree, establishing rationality for most degrees with some notable exceptions.

Contribution

It proves the rationality of the moduli space of plane curves for most degrees, identifying specific degrees where rationality remains uncertain.

Findings

Rationality established for most degrees d

Exceptions identified at degrees 6, 7, 8, 11, 12, 14, 15, 16, 18, 20, 23, 24, 26, 32, 48

Provides a comprehensive classification of rationality for these moduli spaces

Abstract

We prove that the moduli space C(d) of plane curves of degree d (for projective equivalence) is rational except possibly if d= 6, 7, 8, 11, 12, 14, 15, 16, 18, 20, 23, 24, 26, 32, 48.