Geodesic
Equivariant minimal model program
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 3, pp. 461-542

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The purpose of the survey is to systematize a vast amount of information about the minimal model program for varieties with group actions. We discuss the basic methods of the theory and give sketches of the proofs of some principal results. Bibliography: 243 titles. 
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     title = {Equivariant minimal model program},
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Yu. G. Prokhorov. Equivariant minimal model program. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 3, pp. 461-542. http://geodesic.mathdoc.fr/item/RM_2021_76_3_a2/