Arithmetic and topology of classical structures associated to plane quartics

TL;DR

This paper studies the topology and arithmetic of moduli spaces of plane quartics with special structures, computing their cohomology and exploring applications over finite fields.

Contribution

It determines the cohomology of moduli spaces of plane quartics with various marked structures, addressing open questions and exploring arithmetic applications.

Findings

Cohomology of moduli spaces of plane quartics with Cayley octads, Aronhold heptads, Steiner complexes, and G"opel subsets is computed.

Answers to open questions posed by Jesse Wolfson are provided.

Arithmetic applications over finite fields are explored.

Abstract

We consider moduli spaces of plane quartics marked with various structures such as Cayley octads, Aronhold heptads, Steiner complexes and G\"opel subsets and determine their cohomology. This answers a series of questions of Jesse Wolfson. We also explore some arithmetic applications over finite fields.