Volume 14, issue 1 (2010)

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

Volume 29
Issue 2, 549–862
Issue 1, 1–548

Volume 28, 9 issues

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 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Plane sextics via dessins d'enfants

Alex Degtyarev

Geometry & Topology 14 (2010) 393–433
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