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
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