Group Actions on Stacks and Applications

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Projectivity and birational geometry of Bridgeland moduli spaces on an Enriques surface (2014, background): “For a more general and thorough discussion of these issues, see [45].”
Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, unknown): “tions should ignore the G m-action on the line bundles. The issue is treated extensively in the literature. A procedure for removing the redundant action, called rigidiﬁcation, is treated in [ACV03], [Rom05], [AGV08], [AOV08a, Appendix A]. This is foreshadowed by the appendix in [Art74]. Going back ”
Gromov-Witten theory of Deligne-Mumford stacks (2006, methodology): “, if Xis a Deligne–Mumford stack, then X( H is also a Deligne–Mumford stack and the morphism X→X(His ´etale. The notation in [ACV] is XH; here we adopt the better notation X( H proposed by Romagny in [Ro]. This stack X(His called the H-rigidiﬁcation of X. For example, if G→Tis a gerbe banded by H, t”
QUANTUM KIRWAN MORPHISM AND GROMOV-WITTEN INVARIANTS OF QUOTIENTS I (2012, result): “Unfortunately, there seems to be no general construction which guarantees that HomS(X ,Y) is an Artin stack, but partial results are given by Olsson [39], Romagny [44], and Lieblich [29, 2.”