(Log) twisted curves

By Martin Olsson. Compositio Mathematica, 2007

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LOCALIZATION IN GROMOV-WITTEN THEORY AND ORBIFOLD GROMOV-WITTEN THEORY (2011, background): “Then M tw g,n is a smooth algebraic stack, locally of finite type [49].”
Logarithmic Geometry and Moduli (2010, methodology): “The more recent approach of [1] relies on a method introduced in [51], which uses a construction with logarithmic structures.”
QUANTUM KIRWAN MORPHISM AND GROMOV-WITTEN INVARIANTS OF QUOTIENTS I (2012, methodology): “We recall the definitions of twisted curve and twisted stable map to a DeligneMumford stack from Abramovich-Graber-Vistoli [1], Abramovich-Olsson-Vistoli [2], and Olsson [40].”
Expanded Degenerations and Pairs (2011, background): “According to [7, 24] there is an equivalence of categories between logarithmic twisted curves and twisted curves.”
Stable logarithmic maps to Deligne-Faltings pairs I (2010, unknown): “See [Ols07], and [Ols03b, 2.”
Logarithmic Stable Maps (2008, methodology): “As a generalization of log twisted curves ([30]) to a FM type space W/S we define the following.”
Stable logarithmic maps to Deligne-Faltings pairs II (2014, methodology): “We refer to [Kat00], [Moc95], and [Ols07] for more details of log structures on curves.”