Stable maps into the classifying space of the general linear group

TL;DR

This paper proposes a new definition for stable maps into the classifying stack of the general linear group and demonstrates natural boundary morphisms between associated moduli groupoids, supporting the validity of the definition.

Contribution

It introduces a novel definition of stable maps into GL_r and establishes boundary morphisms, advancing the understanding of moduli spaces in algebraic geometry.

Findings

Defined stable maps into GL_r

Constructed natural boundary morphisms

Supported the definition's correctness

Abstract

In this note we give a definition of stable maps into the classifying stack $\BGL_r$ of the general linear group. To support our belief that the definition is the correct one, we show that there are natural boundary morphisms between the moduli groupoids parameterizing stable maps to $\BGL_r$.