A new orbit closure in genus 8?

TL;DR

This paper presents numerical evidence suggesting the existence of a previously unknown 4-dimensional orbit closure in genus 8, related to the unfolding of a specific triangle, expanding understanding of moduli spaces.

Contribution

It introduces a new orbit closure in genus 8, supported by numerical evidence, which was not previously known in the mathematical literature.

Findings

Numerical evidence for a new 4-dimensional orbit closure.

Identification of the orbit closure related to the (3,4,13)-triangle.

Expansion of the classification of orbit closures in moduli spaces.

Abstract

We provide numerical evidence that the orbit closure of the unfolding of the $(3,4,13)$-triangle is a previously unknown 4-dimensional variety.