The discriminant of a space curve is stable

TL;DR

This paper proves that the discriminant of a smooth space curve of genus at least 2 remains stable under the standard action of the special linear group, contributing to the understanding of geometric stability.

Contribution

It establishes the stability of the discriminant for nonsingular space curves of genus ≥ 2 under group actions, a new result in algebraic geometry.

Findings

Discriminant stability proven for genus ≥ 2 space curves

Supports geometric invariant theory in algebraic geometry

Advances understanding of moduli of space curves

Abstract

We prove that the discriminant of a nonsingular space curve of genus $g\geq 2$ is stable with respect to the standard action of the special linear group.