Geometry & Topology Volume 26, issue 1 (2022)

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The Jordan property for local fundamental groups

Lukas Braun, Stefano Filipazzi, Joaquín Moraga and Roberto Svaldi

Geometry & Topology 26 (2022) 283–319

DOI: 10.2140/gt.2022.26.283

Bibliography

1	D Abramovich, J Wang, Equivariant resolution of singularities in characteristic 0, Math. Res. Lett. 4 (1997) 427 MR1453072
2	I V Arzhantsev, S A Gaĭfullin, Cox rings, semigroups, and automorphisms of affine varieties, Mat. Sb. 201 (2010) 3 MR2641086
3	P Belmans, A J de Jong, others, The Stacks project, electronic reference (2005–)
4	C Birkar, Anti-pluricanonical systems on Fano varieties, Ann. of Math. 190 (2019) 345 MR3997127
5	C Birkar, Singularities of linear systems and boundedness of Fano varieties, Ann. of Math. 193 (2021) 347 MR4224714
6	C Birkar, P Cascini, C D Hacon, J McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010) 405 MR2601039
7	L Braun, The local fundamental group of a Kawamata log terminal singularity is finite, Invent. Math. 226 (2021) 845 MR4337973
8	F Campana, Orbifoldes géométriques spéciales et classification biméromorphe des variétés kählériennes compactes, J. Inst. Math. Jussieu 10 (2011) 809 MR2831280
9	M J Collins, On Jordan’s theorem for complex linear groups, J. Group Theory 10 (2007) 411 MR2334748
10	D A Cox, J B Little, H K Schenck, Toric varieties, 124, Amer. Math. Soc. (2011) MR2810322
11	A H Durfee, Neighborhoods of algebraic sets, Trans. Amer. Math. Soc. 276 (1983) 517 MR688959
12	T de Fernex, J Kollár, C Xu, The dual complex of singularities, from: "Higher dimensional algebraic geometry—in honour of Professor Yujiro Kawamata’s sixtieth birthday" (editors K Oguiso, C Birkar, S Ishii, S Takayama), Adv. Stud. Pure Math. 74, Math. Soc. Japan (2017) 103 MR3791210
13	H Flenner, Divisorenklassengruppen quasihomogener Singularitäten, J. Reine Angew. Math. 328 (1981) 128 MR636200
14	H Flenner, M Zaidenberg, Locally nilpotent derivations on affine surfaces with a ℂ^∗–action, Osaka J. Math. 42 (2005) 931 MR2196000
15	R M Fossum, The divisor class group of a Krull domain, 74, Springer (1973) MR0382254
16	A Fujiki, R Kobayashi, S Lu, On the fundamental group of certain open normal surfaces, Saitama Math. J. 11 (1993) 15 MR1259272
17	M Goresky, R MacPherson, Morse theory and intersection homology theory, from: "Analysis and topology on singular spaces, II–III", Astérisque 101–102, Soc. Math. France (1983) 135 MR737930
18	M Goresky, R MacPherson, Stratified Morse theory, 14, Springer (1988) MR932724
19	R M Goresky, Whitney stratified chains and cochains, Trans. Amer. Math. Soc. 267 (1981) 175 MR621981
20	A Grassi, J Kollár, Reduction to special flips, from: "Flips and abundance for algebraic threefolds" (editor J Kollár), Astérisque 211, Soc. Math. France (1992) 193 MR1225842
21	D Greb, S Kebekus, T Peternell, Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of abelian varieties, Duke Math. J. 165 (2016) 1965 MR3522654
22	R V Gurjar, D Q Zhang, π₁ of smooth points of a log del Pezzo surface is finite, I, J. Math. Sci. Univ. Tokyo 1 (1994) 137 MR1298542
23	R V Gurjar, D Q Zhang, π₁ of smooth points of a log del Pezzo surface is finite, II, J. Math. Sci. Univ. Tokyo 2 (1995) 165 MR1348027
24	J Han, J Liu, V V Shokurov, ACC for minimal log discrepancies of exceptional singularities, preprint (2019) arXiv:1903.04338
25	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
26	C Jordan, Mémoire sur une application de la théorie des substitutions à l’étude des équations différentielles linéaires, Bull. Soc. Math. France 2 (1873/74) 100 MR1503686
27	M Kapovich, J Kollár, Fundamental groups of links of isolated singularities, J. Amer. Math. Soc. 27 (2014) 929 MR3230815
28	S Keel, J McKernan, Rational curves on quasi-projective surfaces, 669, Amer. Math. Soc. (1999) MR1610249
29	J Kollár, New examples of terminal and log canonical singularities, preprint (2011) arXiv:1107.2864
30	J Kollár, Singularities of the minimal model program, 200, Cambridge Univ. Press (2013) MR3057950
31	J Kollár, S Mori, Birational geometry of algebraic varieties, 134, Cambridge Univ. Press (1998) MR1658959
32	A Laface, A Liendo, J Moraga, The fundamental group of a log terminal 𝕋–variety, Eur. J. Math. 5 (2019) 937 MR3993273
33	J Milnor, Singular points of complex hypersurfaces, 61, Princeton Univ. Press (1968) MR0239612
34	J Moraga, On minimal log discrepancies and Kollár components, preprint (2018) arXiv:1810.10137
35	J Moraga, Fano-type surfaces with large cyclic automorphisms, Forum Math. Sigma 9 (2021) MR4298025
36	D Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Inst. Hautes Études Sci. Publ. Math. 9 (1961) 5 MR153682
37	V L Popov, On the Makar–Limanov, Derksen invariants, and finite automorphism groups of algebraic varieties, from: "Affine algebraic geometry" (editors D Daigle, R Ganong, M Koras), CRM Proc. Lecture Notes 54, Amer. Math. Soc. (2011) 289 MR2768646
38	Y G Prokhorov, Blow-ups of canonical singularities, from: "Algebra" (editor Y Bahturin), de Gruyter (2000) 301 MR1754677
39	Y G Prokhorov, V V Shokurov, The first fundamental theorem on complements: from global to local, Izv. Ross. Akad. Nauk Ser. Mat. 65 (2001) 99 MR1892905
40	Y G Prokhorov, C Shramov, Jordan property for groups of birational selfmaps, Compos. Math. 150 (2014) 2054 MR3292293
41	Y G Prokhorov, C Shramov, Jordan property for Cremona groups, Amer. J. Math. 138 (2016) 403 MR3483470
42	V V Shokurov, Three-dimensional log perestroikas, Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992) 105 MR1162635
43	D E Speyer, Equivariant normalization?, MathOverflow post (2013)
44	U Storch, Über die Divisorenklassengruppen normaler komplexanalytischer Algebren, Math. Ann. 183 (1969) 93 MR257070
45	H Sumihiro, Equivariant completion, J. Math. Kyoto Univ. 14 (1974) 1 MR337963
46	Z Tian, C Xu, Finiteness of fundamental groups, Compos. Math. 153 (2017) 257 MR3604863
47	C Xu, Finiteness of algebraic fundamental groups, Compos. Math. 150 (2014) 409 MR3187625
48	C Xu, Z Zhuang, Uniqueness of the minimizer of the normalized volume function, Camb. J. Math. 9 (2021) 149 MR4325260