Degenerations of twisted maps to algebraic stacks

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.

arXiv comment36 pages, comments very welcome! v2: corrected a mistake, added an additional assumption in the main theorem; we require the algebraic stack to be a quotient stack. v3: added a more detailed discussion of contractions for stacky surfaces, improved exposition