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

Volume 27
Issue 9, 3387–3831
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

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 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
Unexpected Stein fillings, rational surface singularities and plane curve arrangements

Olga Plamenevskaya and Laura Starkston

Geometry & Topology 27 (2023) 1083–1202
Bibliography
1 N A’Campo, Le groupe de monodromie du déploiement des singularités isolées de courbes planes, I, Math. Ann. 213 (1975) 1 MR377108
2 S Akbulut, B Ozbagci, Lefschetz fibrations on compact Stein surfaces, Geom. Topol. 5 (2001) 319 MR1825664
3 A Akhmedov, B Ozbagci, Singularity links with exotic Stein fillings, J. Singul. 8 (2014) 39 MR3213526
4 A Akhmedov, B Ozbagci, Exotic Stein fillings with arbitrary fundamental group, Geom. Dedicata 195 (2018) 265 MR3820506
5 M Artin, Algebraic construction of Brieskorn’s resolutions, J. Algebra 29 (1974) 330 MR354665
6 D Auroux, A stable classification of Lefschetz fibrations, Geom. Topol. 9 (2005) 203 MR2115673
7 R İ Baykur, N Monden, J Van Horn-Morris, Positive factorizations of mapping classes, Algebr. Geom. Topol. 17 (2017) 1527 MR3677934
8 M Bhupal, K Ono, Symplectic fillings of links of quotient surface singularities, Nagoya Math. J. 207 (2012) 1 MR2957141
9 M Bhupal, A I Stipsicz, Smoothings of singularities and symplectic topology, from: "Deformations of surface singularities" (editors A Némethi, Á Szilárd), Bolyai Soc. Math. Stud. 23, János Bolyai Math. Soc. (2013) 57 MR3203575
10 F A Bogomolov, B de Oliveira, Stein small deformations of strictly pseudoconvex surfaces, from: "Birational algebraic geometry" (editors Y Kawamata, V V Shokurov), Contemp. Math. 207, Amer. Math. Soc. (1997) 25 MR1462922
11 C Caubel, A Némethi, P Popescu-Pampu, Milnor open books and Milnor fillable contact 3–manifolds, Topology 45 (2006) 673 MR2218761
12 D C Cohen, A I Suciu, The braid monodromy of plane algebraic curves and hyperplane arrangements, Comment. Math. Helv. 72 (1997) 285 MR1470093
13 Y Eliashberg, On symplectic manifolds with some contact properties, J. Differential Geom. 33 (1991) 233 MR1085141
14 H Endo, T E Mark, J Van Horn-Morris, Monodromy substitutions and rational blowdowns, J. Topol. 4 (2011) 227 MR2783383
15 J B Etnyre, Planar open book decompositions and contact structures, Int. Math. Res. Not. 2004 (2004) 4255 MR2126827
16 B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
17 E Fossati, Contact surgery on the Hopf link: classification of fillings, preprint (2019) arXiv:1905.13026
18 D Gay, T E Mark, Convex plumbings and Lefschetz fibrations, J. Symplectic Geom. 11 (2013) 363 MR3100798
19 P Ghiggini, M Golla, O Plamenevskaya, Surface singularities and planar contact structures, Ann. Inst. Fourier (Grenoble) 70 (2020) 1791 MR4245589
20 R E Gompf, A I Stipsicz, 4–Manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
21 J E Goodman, Proof of a conjecture of Burr, Grünbaum, and Sloane, Discrete Math. 32 (1980) 27 MR588905
22 G M Greuel, J Steenbrink, On the topology of smoothable singularities, from: "Singularities, I" (editor P Orlik), Proc. Sympos. Pure Math. 40, Amer. Math. Soc. (1983) 535 MR713090
23 B Grünbaum, Configurations of points and lines, 103, Amer. Math. Soc. (2009) MR2510707
24 E Hironaka, Generalized lantern relations and planar line arrangements, from: "Computational algebraic and analytic geometry" (editors M Seppälä, E Volcheck), Contemp. Math. 572, Amer. Math. Soc. (2012) 113 MR2953827
25 K Honda, W H Kazez, G Matić, Right-veering diffeomorphisms of compact surfaces with boundary, Invent. Math. 169 (2007) 427 MR2318562
26 T de Jong, D van Straten, On the deformation theory of rational surface singularities with reduced fundamental cycle, J. Algebraic Geom. 3 (1994) 117 MR1242008
27 T de Jong, D van Straten, Deformation theory of sandwiched singularities, Duke Math. J. 95 (1998) 451 MR1658768
28 A Kaloti, Stein fillings of planar open books, preprint (2013) arXiv:1311.0208
29 J Kollár, Toward moduli of singular varieties, Compos. Math. 56 (1985) 369 MR814554
30 J Kollár, Flips, flops, minimal models, etc., from: "Surveys in differential geometry" (editors C C Hsiung, S T Yau), Lehigh Univ. (1991) 113 MR1144527
31 H B Laufer, Normal two-dimensional singularities, 71, Princeton Univ. Press (1971) MR0320365
32 H B Laufer, Taut two-dimensional singularities, Math. Ann. 205 (1973) 131 MR333238
33 H B Laufer, On μ for surface singularities, from: "Several complex variables, I" (editor R O Wells Jr.), Proc. Sympos. Pure Math. 30, Amer. Math. Soc. (1977) 45 MR0450287
34 P Lisca, On symplectic fillings of lens spaces, Trans. Amer. Math. Soc. 360 (2008) 765 MR2346471
35 S Lisi, C Wendl, Spine removal surgery and the geography of symplectic fillings, Michigan Math. J. 70 (2021) 403 MR4278702
36 D Margalit, J McCammond, Geometric presentations for the pure braid group, J. Knot Theory Ramifications 18 (2009) 1 MR2490001
37 H Matsumoto, Générateurs et relations des groupes de Weyl généralisés, C. R. Acad. Sci. Paris 258 (1964) 3419 MR183818
38 D McDuff, The structure of rational and ruled symplectic 4–manifolds, J. Amer. Math. Soc. 3 (1990) 679 MR1049697
39 J Milnor, Singular points of complex hypersurfaces, 61, Princeton Univ. Press (1968) MR0239612
40 B Moishezon, M Teicher, Braid group technique in complex geometry, I : Line arrangements in P2, from: "Braids" (editors J S Birman, A Libgober), Contemp. Math. 78, Amer. Math. Soc. (1988) 425 MR975093
41 B Moishezon, M Teicher, Braid group technique in complex geometry, II : From arrangements of lines and conics to cuspidal curves, from: "Algebraic geometry" (editors S Bloch, I Dolgachev, W Fulton), Lecture Notes in Math. 1479, Springer (1991) 131 MR1181212
42 A Némethi, Five lectures on normal surface singularities, from: "Low dimensional topology" (editors K Böröczky Jr., W Neumann, A Stipsicz), Bolyai Soc. Math. Stud. 8, János Bolyai Math. Soc. (1999) 269 MR1747271
43 A Némethi, Some meeting points of singularity theory and low dimensional topology, from: "Deformations of surface singularities" (editors A Némethi, Á Szilárd), Bolyai Soc. Math. Stud. 23, János Bolyai Math. Soc. (2013) 109 MR3203577
44 A Némethi, P Popescu-Pampu, On the Milnor fibers of sandwiched singularities, Int. Math. Res. Not. 2010 (2010) 1041 MR2601064
45 A Némethi, P Popescu-Pampu, On the Milnor fibres of cyclic quotient singularities, Proc. Lond. Math. Soc. 101 (2010) 554 MR2679701
46 A Némethi, M Tosun, Invariants of open books of links of surface singularities, Studia Sci. Math. Hungar. 48 (2011) 135 MR2868183
47 W D Neumann, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc. 268 (1981) 299 MR632532
48 K Niederkrüger, C Wendl, Weak symplectic fillings and holomorphic curves, Ann. Sci. École Norm. Sup. 44 (2011) 801 MR2931519
49 H Ohta, K Ono, Symplectic fillings of the link of simple elliptic singularities, J. Reine Angew. Math. 565 (2003) 183 MR2024651
50 H Ohta, K Ono, Simple singularities and symplectic fillings, J. Differential Geom. 69 (2005) 1 MR2169581
51 P Ozsváth, Z Szabó, On the Floer homology of plumbed three-manifolds, Geom. Topol. 7 (2003) 185 MR1988284
52 H Park, J Park, D Shin, G Urzúa, Milnor fibers and symplectic fillings of quotient surface singularities, Adv. Math. 329 (2018) 1156 MR3783436
53 H C Pinkham, Deformations of algebraic varieties with Gm action, 20, Soc. Math. France (1974) MR0376672
54 O Plamenevskaya, On Legendrian surgeries between lens spaces, J. Symplectic Geom. 10 (2012) 165 MR2926993
55 P Popescu-Pampu, On the smoothings of non-normal isolated surface singularities, J. Singul. 12 (2015) 164 MR3317148
56 P Popescu-Pampu, Complex singularities and contact topology, Winter Braids Lect. Notes 3 (2016) MR3707744
57 D Ruberman, L Starkston, Topological realizations of line arrangements, Int. Math. Res. Not. 2019 (2019) 2295 MR3942162
58 S Schönenberger, Determining symplectic fillings from planar open books, J. Symplectic Geom. 5 (2007) 19 MR2371183
59 L Starkston, Classifications and applications of symplectic fillings of Seifert fibered spaces over S2, PhD thesis, University of Texas at Austin (2015)
60 A I Stipsicz, On the geography of Stein fillings of certain 3–manifolds, Michigan Math. J. 51 (2003) 327 MR1992949
61 M Symington, Symplectic rational blowdowns, J. Differential Geom. 50 (1998) 505 MR1690738
62 S Tendian, Surfaces of degree d with sectional genus g in d+1g and deformations of cones, Duke Math. J. 65 (1992) 157 MR1148988
63 W P Thurston, A norm for the homology of 3–manifolds, Mem. Amer. Math. Soc. 339, Amer. Math. Soc. (1986) 99 MR823443
64 G N Tyurina, Locally semi-universal flat deformations of isolated singularities of complex spaces, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969) 1026 MR0252685
65 C Wendl, Strongly fillable contact manifolds and J–holomorphic foliations, Duke Math. J. 151 (2010) 337 MR2605865