Volume 26, issue 1 (2022)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
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 –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