Degenerations of twisted maps to algebraic stacks

TL;DR

This paper introduces a new definition for twisted maps to quotient stacks with projective moduli spaces and proves that the associated functor satisfies a key properness criterion.

Contribution

It provides a formal definition of twisted maps to algebraic stacks and establishes their properness properties via the valuative criterion.

Findings

Defined twisted maps to quotient stacks with projective moduli.

Proved the functor satisfies the existence part of the valuative criterion for properness.

Abstract

We give a definition of twisted map to a quotient stack with projective good moduli space, and we show that the resulting functor satisfies the existence part of the valuative criterion for properness.