Moduli Spaces of Shtukas over the Projective Line

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 ${\mathbb{P}}^1$.

21 pages