Moduli Spaces of Shtukas over the Projective Line

TL;DR

This paper explicitly describes the equations of moduli spaces of Drinfeld shtukas over the projective line with various level structures, analyzing their geometric properties and invariants for certain divisors.

Contribution

It provides explicit equations for these moduli spaces and investigates their invariants, especially for high-degree divisors and specific level structures.

Findings

Moduli spaces are relative surfaces for high-degree divisors.

Explicit equations are derived for different level structures.

Invariants of the moduli space with $\Gamma_0(N)$ level are studied for degree 4 divisors.

Abstract

We provide explicit equations for moduli spaces of Drinfeld shtukas over the projective line with $\Gamma(N)$, $\Gamma_1(N)$ and $\Gamma_0(N)$ level structures, where $N$ is an effective divisor on $\mathbb{P}^1$. If the degree of $N$ is high enough, these moduli spaces are relative surfaces. We study some invariants of the moduli space of shtukas with $\Gamma_0(N)$ level structure for several degree $4$ divisors on $\mathbb{P}^1$.