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Plane curves and their fundamental groups: Generalizations of Uludağ's construction

David Garber

Algebraic & Geometric Topology 3 (2003) 593–622
Bibliography
1 M Amram, D Garber, M Teicher, Fundamental groups of tangent conic-line arrangements with singularities up to order 6, Math. Z. 256 (2007) 837 MR2308894
2 M Amram, M Teicher, Braid monodromy of special curves, J. Knot Theory Ramifications 10 (2001) 171 MR1822489
3 E Artal-Bartolo, Sur les couples de Zariski, J. Algebraic Geom. 3 (1994) 223 MR1257321
4 E Artal Bartolo, Fundamental group of a class of rational cuspidal curves, Manuscripta Math. 93 (1997) 273 MR1457728
5 E Artal Bartolo, J Carmona Ruber, Zariski pairs, fundamental groups and Alexander polynomials, J. Math. Soc. Japan 50 (1998) 521 MR1626409
6 E Artal, J Carmona, J I Cogolludo, H Tokunaga, Sextics with singular points in special position, J. Knot Theory Ramifications 10 (2001) 547 MR1831676
7 E Artal Bartolo, H Tokunaga, Zariski pairs of index 19 and Mordell–Weil groups of $K3$ surfaces, Proc. London Math. Soc. $(3)$ 80 (2000) 127 MR1719168
8 O Chisini, Sulla identita birazionale delle funzioni algebriche di due variabili dotate di una medesima curva di diramazione, Ist. Lombardo Sci. Lett. Cl. Sci. Mat. Nat. Rend. $(3)$ 8(77) (1944) 339 MR0019351
9 A I Degtyarev, Quintics in $\mathbb{C}\mathrm{P}^2$ with nonabelian fundamental group, Algebra i Analiz 11 (1999) 130 MR1734350
10 H Flenner, M Zaidenberg, Rational cuspidal plane curves of type $(d,d-3)$, Math. Nachr. 210 (2000) 93 MR1738940
11 T Fujita, On the topology of noncomplete algebraic surfaces, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982) 503 MR687591
12 D Garber, M Teicher, The fundamental group's structure of the complement of some configurations of real line arrangements, from: "Complex analysis and algebraic geometry", de Gruyter (2000) 173 MR1760878
13 D Garber, M Teicher, U Vishne, $\pi_1$–classification of real arrangements with up to eight lines, Topology 42 (2003) 265 MR1928653
14 V S Kulikov, On Chisini's conjecture, Izv. Ross. Akad. Nauk Ser. Mat. 63 (1999) 83 MR1748562
15 V S Kulikov, M Taĭkher, Braid monodromy factorizations and diffeomorphism types, Izv. Ross. Akad. Nauk Ser. Mat. 64 (2000) 89 MR1770673
16 J Milnor, Morse theory, Annals of Mathematics Studies 51, Princeton University Press (1963) MR0163331
17 B Moishezon, M Teicher, Braid group technique in complex geometry II: From arrangements of lines and conics to cuspidal curves, from: "Algebraic geometry (Chicago, IL, 1989)", Lecture Notes in Math. 1479, Springer (1991) 131 MR1181212
18 M Nagata, On rational surfaces I: Irreducible curves of arithmetic genus 0 or 1, Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 32 (1960) 351 MR0126443
19 M Namba, Geometry of projective algebraic curves, Monographs and Textbooks in Pure and Applied Mathematics 88, Marcel Dekker (1984) MR768929
20 M Oka, Two transforms of plane curves and their fundamental groups, J. Math. Sci. Univ. Tokyo 3 (1996) 399 MR1424436
21 M Oka, Flex curves and their applications, Geom. Dedicata 75 (1999) 67 MR1680188
22 M Oka, A new Alexander-equivalent Zariski pair, Acta Math. Vietnam. 27 (2002) 349 MR1979814
23 R Randell, The fundamental group of the complement of a union of complex hyperplanes, Invent. Math. 69 (1982) 103 MR671654
24 J J Rotman, An introduction to the theory of groups, Graduate Texts in Mathematics 148, Springer (1995) MR1307623
25 J A Schafer, Extensions of nilpotent groups, Houston J. Math. 21 (1995) 1 MR1331240
26 I Shimada, A weighted version of Zariski's hyperplane section theorem and fundamental groups of complements of plane curves arXiv:alg-geom/9505004
27 I Shimada, A note on Zariski pairs, Compositio Math. 104 (1996) 125 MR1421396
28 I Shimada, Fundamental groups of complements to singular plane curves, Amer. J. Math. 119 (1997) 127 MR1428061
29 H Tokunaga, A remark on E. Artal–Bartolo's paper: “On Zariski pairs”, Kodai Math. J. 19 (1996) 207 MR1397422
30 H Tokunaga, Some examples of Zariski pairs arising from certain elliptic $K3$ surfaces, Math. Z. 227 (1998) 465 MR1612673
31 H Tokunaga, Some examples of Zariski pairs arising from certain elliptic $K3$ surfaces II: Degtyarev's conjecture, Math. Z. 230 (1999) 389 MR1676710
32 A M Uludağ, Groupes fondamentaux d'une famille de courbes rationnelles cuspidales, PhD thesis, Institut Fourier, Universite de Grenoble I (2000)
33 A M Uludağ, More Zariski pairs and finite fundamental groups of curve complements, Manuscripta Math. 106 (2001) 271 MR1869220
34 E R V Kampen, On the Fundamental Group of an Algebraic Curve, Amer. J. Math. 55 (1933) 255 MR1506962
35 M Zaĭdenberg, Exotic algebraic structures on affine spaces, Algebra i Analiz 11 (1999) 3 MR1734345
36 O Zariski, On the Problem of Existence of Algebraic Functions of Two Variables Possessing a Given Branch Curve, Amer. J. Math. 51 (1929) 305 MR1506719
37 O Zariski, The Topological Discriminant Group of a Riemann Surface of Genus $p$, Amer. J. Math. 59 (1937) 335 MR1507244