Volume 26, issue 1 (2022)

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

Volume 28
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

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 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
Inner geometry of complex surfaces: a valuative approach

André Belotto da Silva, Lorenzo Fantini and Anne Pichon

Geometry & Topology 26 (2022) 163–219
DOI: 10.2140/gt.2022.26.163
Bibliography
1 M Aymé, Les Contes du chat perché, Gallimard (1946)
2 M Baker, J Nicaise, Weight functions on Berkovich curves, Algebra Number Theory 10 (2016) 2053 MR3582013
3 A Belotto da Silva, E Bierstone, V Grandjean, P D Milman, Resolution of singularities of the cotangent sheaf of a singular variety, Adv. Math. 307 (2017) 780 MR3590532
4 A Belotto da Silva, L Fantini, A Pichon, On Lipschitz normally embedded complex surface germs, preprint (2020) arXiv:2006.01773
5 V G Berkovich, Spectral theory and analytic geometry over non-Archimedean fields, 33, Amer. Math. Soc. (1990) MR1070709
6 A Bernig, A Lytchak, Tangent spaces and Gromov–Hausdorff limits of subanalytic spaces, J. Reine Angew. Math. 608 (2007) 1 MR2339466
7 L Birbrair, W D Neumann, A Pichon, The thick-thin decomposition and the bilipschitz classification of normal surface singularities, Acta Math. 212 (2014) 199 MR3207758
8 R Bondil, L D T, Résolution des singularités de surfaces par éclatements normalisés (multiplicité, multiplicité polaire, et singularités minimales), from: "Trends in singularities" (editors A Libgober, M Tibăr), Birkhäuser (2002) 31 MR1900780
9 J Briançon, J P Speder, La trivialité topologique n’implique pas les conditions de Whitney, C. R. Acad. Sci. Paris Sér. A-B 280 (1975) MR425165
10 J Cheeger, On the Hodge theory of Riemannian pseudomanifolds, from: "Geometry of the Laplace operator" (editors R Osserman, A Weinstein), Proc. Sympos. Pure Math. XXXVI, Amer. Math. Soc. (1980) 91 MR573430
11 S Corry, D Perkinson, Divisors and sandpiles: an introduction to chip-firing, Amer. Math. Soc. (2018) MR3793659
12 M Escher, Ascending and descending, lithograph (1960)
13 L Fantini, Normalized Berkovich spaces and surface singularities, Trans. Amer. Math. Soc. 370 (2018) 7815 MR3852450
14 L Fantini, C Favre, M Ruggiero, Links of sandwiched surface singularities and self-similarity, Manuscripta Math. 162 (2020) 23 MR4079797
15 L Fantini, D Turchetti, Galois descent of semi-affinoid spaces, Math. Z. 290 (2018) 1085 MR3856846
16 C Favre, Holomorphic self-maps of singular rational surfaces, Publ. Mat. 54 (2010) 389 MR2675930
17 C Favre, M Jonsson, The valuative tree, 1853, Springer (2004) MR2097722
18 E R García Barroso, P D González Pérez, P Popescu-Pampu, The valuative tree is the projective limit of Eggers–Wall trees, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 113 (2019) 4051 MR3999063
19 E R García Barroso, P D González Pérez, P Popescu-Pampu, M Ruggiero, Ultrametric properties for valuation spaces of normal surface singularities, Trans. Amer. Math. Soc. 372 (2019) 8423 MR4029701
20 E García Barroso, B Teissier, Concentration multi-échelles de courbure dans des fibres de Milnor, Comment. Math. Helv. 74 (1999) 398 MR1710694
21 W Gignac, M Ruggiero, Local dynamics of non-invertible maps near normal surface singularities, 1337, Amer. Math. Soc. (2021) MR4321202
22 G Gonzalez-Sprinberg, Résolution de Nash des points doubles rationnels, Ann. Inst. Fourier (Grenoble) 32 (1982) 111 MR662442
23 G M Greuel, Der Gauss–Manin–Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten, Math. Ann. 214 (1975) 235 MR396554
24 W C Hsiang, V Pati, L2–cohomology of normal algebraic surfaces, I, Invent. Math. 81 (1985) 395 MR807064
25 M Jonsson, Dynamics of Berkovich spaces in low dimensions, from: "Berkovich spaces and applications" (editors A Ducros, C Favre, J Nicaise), Lecture Notes in Math. 2119, Springer (2015) 205 MR3330767
26 K Kurdyka, P Orro, Distance géodésique sur un sous-analytique, Rev. Mat. Univ. Complut. Madrid 10 (1997) 173 MR1485298
27 H B Laufer, Normal two-dimensional singularities, 71, Princeton Univ. Press (1971) MR0320365
28 L D T, Computation of the Milnor number of an isolated singularity of a complete intersection, Funkcional. Anal. i Priložen. 8 (1974) 45 MR0350064
29 L D T, Geometry of complex surface singularities, from: "Singularities" (editors J P Brasselet, T Suwa), Adv. Stud. Pure Math. 29, Kinokuniya (2000) 163 MR1819635
30 L D T, B Teissier, Variétés polaires locales et classes de Chern des variétés singulières, Ann. of Math. 114 (1981) 457 MR634426
31 D B Massey, Hypercohomology of Milnor fibres, Topology 35 (1996) 969 MR1404920
32 Y Matsumoto, J M Montesinos-Amilibia, Pseudo-periodic maps and degeneration of Riemann surfaces, 2030, Springer (2011) MR2839459
33 H Maugendre, F Michel, On the growth behaviour of Hironaka quotients, J. Singul. 20 (2020) 31 MR4066295
34 F Michel, Jacobian curves for normal complex surfaces, from: "Singularities, II" (editors J P Brasselet, J L Cisneros-Molina, D Massey, J Seade, B Teissier), Contemp. Math. 475, Amer. Math. Soc. (2008) 135 MR2454364
35 T Mostowski, Lipschitz equisingularity, Dissertationes Math. (Rozprawy Mat.) 243 (1985) 46 MR808226
36 M Nagase, Remarks on the L2–cohomology of singular algebraic surfaces, J. Math. Soc. Japan 41 (1989) 97 MR972167
37 W D Neumann, H M l Pedersen, A Pichon, A characterization of Lipschitz normally embedded surface singularities, J. Lond. Math. Soc. 101 (2020) 612 MR4093968
38 A Parusiński, Lipschitz properties of semi-analytic sets, Ann. Inst. Fourier (Grenoble) 38 (1988) 189 MR978246
39 A Pichon, W D Neumann, A non-normally embedded complex normal surface with normally embedded reduced tangent cone, MR3988673
40 M Spivakovsky, Sandwiched singularities and desingularization of surfaces by normalized Nash transformations, Ann. of Math. 131 (1990) 411 MR1053487
41 B Teissier, Variétés polaires, II : Multiplicités polaires, sections planes, et conditions de Whitney, from: "Algebraic geometry" (editors J M Aroca, R Buchweitz, M Giusti, M Merle), Lecture Notes in Math. 961, Springer (1982) 314 MR708342
42 O Zariski, The reduction of the singularities of an algebraic surface, Ann. of Math. 40 (1939) 639 MR159