Geometry & Topology Volume 14, issue 1 (2010)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Plane sextics via dessins d'enfants

Alex Degtyarev

Geometry & Topology 14 (2010) 393–433

DOI: 10.2140/gt.2010.14.393

Bibliography

1	E Artal Bartolo, J Carmona Ruber, J I Cogolludo Agustín, Braid monodromy and topology of plane curves, Duke Math. J. 118 (2003) 261 MR1980995
2	A Degtyarev, Isotopic classification of complex plane projective curves of degree $5$, Algebra i Analiz 1 (1989) 78 MR1027461
3	A Degtyarev, Quintics in $\mathbf{C}\mathrm{P}^2$ with nonabelian fundamental group, Algebra i Analiz 11 (1999) 130 MR1734350
4	A Degtyarev, Fundamental groups of symmetric sextics, J. Math. Kyoto Univ. 48 (2008) 765 MR2513586
5	A Degtyarev, Oka's conjecture on irreducible plane sextics, J. Lond. Math. Soc. $(2)$ 78 (2008) 329 MR2439628
6	A Degtyarev, On deformations of singular plane sextics, J. Algebraic Geom. 17 (2008) 101 MR2357681
7	A Degtyarev, Stable symmetries of plane sextics, Geom. Dedicata 137 (2008) 199 MR2449152
8	A Degtyarev, Fundamental groups of symmetric sextics. II, Proc. London Math. Soc. (3) 99 (2009) 353
9	A Degtyarev, Irreducible plane sextics with large fundamental groups, J. Math. Soc. Japan 61 (2009) 1131
10	A Degtyarev, Zariski $k$–plets via dessins d'enfants, Comment. Math. Helv. 84 (2009) 639 MR2507257
11	A Degtyarev, I Itenberg, V Kharlamov, On deformation types of real elliptic surfaces, Amer. J. Math. 130 (2008) 1561 MR2464028
12	A Degtyarev, M Oka, A plane sextic with finite fundamental group, from: "Proc. of Niigata–Toyama Conferences 2007", to appear in Adv. Stud. Pure Math., Math. Soc. Japan arXiv:0711.3067
13	C Eyral, M Oka, On the fundamental groups of the complements of plane singular sextics, J. Math. Soc. Japan 57 (2005) 37 MR2114719
14	C Eyral, M Oka, Alexander-equivalent Zariski pairs of irreducible sextics arXiv:0811.2310
15	C Eyral, M Oka, On the geometry of certain irreducible non-torus plane sextics, to appear in Kodai Math. J.
16	C Eyral, M Oka, A proof of a conjecture of Degtyarev on non-torus plane sextics, from: "Proc. of Niigata–Toyama Conferences 2007", to appear in Adv. Stud. Pure Math., Math. Soc. Japan
17	T Fujita, On the topology of noncomplete algebraic surfaces, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982) 503 MR687591
18	GAP Group, \ttGAP – Groups, Algorithms, and Programming, Version 4.4.10 (2007)
19	H Ishida, H Tokunaga, Triple covers of algebraic surfaces and a generalization of Zariski's example, from: "Proc. of Niigata–Toyama Conferences 2007", to appear in Adv. Stud. Pure Math., Math. Soc. Japan
20	E R van Kampen, On the fundamental group of an algebraic curve, Amer. J. Math. 55 (1933) 255 MR1506962
21	E Looijenga, The complement of the bifurcation variety of a simple singularity, Invent. Math. 23 (1974) 105 MR0422675
22	S Y Orevkov, Riemann existence theorem and construction of real algebraic curves, Ann. Fac. Sci. Toulouse Math. $(6)$ 12 (2003) 517 MR2060598
23	A Özgüner, Classical Zariski pairs with nodes, dissertation, Bilkent University (2007)
24	U Persson, Double sextics and singular $K3$ surfaces, from: "Algebraic geometry, Sitges (Barcelona), 1983" (editors E Casas-Alvero, G E Welters, S Xambó-Descamps), Lecture Notes in Math. 1124, Springer (1985) 262 MR805337
25	I Shimada, Lattice Zariski pairs of plane sextic curves and splitting curves for double plane sextics, to appear in Michigan Math. J.
26	I Shimada, On the connected components of the moduli of polarized $K3$ surfaces, Preprint
27	J G Yang, Sextic curves with simple singularities, Tohoku Math. J. $(2)$ 48 (1996) 203 MR1387816