A relative GAGA principle for families of curves

Abstract

We prove a relative GAGA principle for families of curves, showing: (i) analytic families of pointed curves whose fibres have finite automorphism groups are algebraizable; and (ii) analytic birational models of M g , n possessing modular interpretations with the finite automorphism property are algebraizable. This is accomplished by extending some well-known GAGA results for proper schemes to non-separated Deligne–Mumford stacks.