A GIT Construction of Moduli Spaces of Stable Maps in Positive Characteristic

TL;DR

This paper extends the construction of moduli spaces of stable maps via GIT from complex numbers to more general base fields, broadening the applicability of the method.

Contribution

It generalizes the GIT construction of moduli spaces of stable maps to arbitrary base fields, removing the previous restriction to complex numbers.

Findings

Constructed coarse moduli spaces over general base fields

Extended GIT techniques to positive characteristic

Maintained properties of moduli spaces in broader settings

Abstract

In a previous paper, the author and David Swinarski constructed the moduli spaces of stable maps, \bar M_g,n(P^r,d), via geometric invariant theory (GIT). That paper required the base field to be the complex numbers, a restriction which this paper removes: here the coarse moduli spaces of stable maps are constructed via GIT over a more general base.