Mumford, Fogarty & Kirwan 1994, Converse 1.13. NB: even though the result is stated for a smooth variety, the proof there is valid for a locally factorial one. Mumford, David; Fogarty, John; Kirwan, Frances (1994). Geometric invariant theory. Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)]. Vol. 34 (3rd ed.). Berlin, New York: Springer-Verlag. ISBN978-3-540-56963-3. MR1304906.