Abstract:
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.
This publication is cited in the following 9 articles:
Yuri Prokhorov, “On the birational geometry of Q-Fano threefolds of large Fano index, I”, Ann Univ Ferrara, 70:3 (2024), 955
Anastasia V. Vikulova, “Birational automorphism groups of Severi–Brauer surfaces over the field of rational numbers”, Int. Math. Res. Not. IMRN, 2024, 1–17
Yuri G. Prokhorov, Constantin A. Shramov, “Jordan Property for the Cremona Group over a Finite Field”, Proc. Steklov Inst. Math., 320 (2023), 278–289
A. A. Avilov, “Birational rigidity of G-del Pezzo threefolds of degree 2”, Sb. Math., 214:6 (2023), 757–792
Yu. Prokhorov, “Rationality of Fano threefolds with terminal Gorenstein singularities, II”, Rend. Circ. Mat. Palermo (2), 72:3 (2023), 1797–1821
Yu. Prokhorov, “Embeddings of the symmetric groups to the space Cremona group”, Birational Geometry, Kähler–Einstein Metrics and Degenerations, Springer Proc. Math. Stat., 409, 2023, 749–762
Yu. G. Prokhorov, “Trekhmernye mnogoobraziya Fano”, Lekts. kursy NOTs, 31, MIAN, M., 2022, 3–154
Yu. G. Prokhorov, С. A. Shramov, “Finite groups of bimeromorphic self-maps of nonuniruled Kähler threefolds”, Sb. Math., 213:12 (2022), 1695–1714
Yu. Prokhorov, “Conic bundle structures on Q-Fano threefolds”, Electronic Research Archive, 30:5 (2022), 1881–1897
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