Geometry & Topology Volume 26, issue 1 (2022)

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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