Proper good quotients for Gₘ-actions

We give an algebraic proof of a result, due to Bialynicki-Birula and Sommese, characterizing the invariant open subsets of a normal proper variety equipped with a Gₘ-action that admit a proper good quotient. A major ingredient is the existence result for moduli spaces of algebraic stacks due to Alper, Halpern-Leistner and Heinloth.