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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  ,  npossessing 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.

A relative GAGA principle for families of curves