Volume 5, issue 2 (2005)

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

Volume 25
Issue 7, 3789–4436
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Some analogs of Zariski's Theorem on nodal line arrangements

A D Raza Choudary, Alexandru Dimca and Ştefan Papadima

Algebraic & Geometric Topology 5 (2005) 691–711
Bibliography
1 M Bestvina, N Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445 MR1465330
2 D C Cohen, G Denham, A I Suciu, Torsion in Milnor fiber homology, Algebr. Geom. Topol. 3 (2003) 511 MR1997327
3 D C Cohen, A Dimca, P Orlik, Nonresonance conditions for arrangements, Ann. Inst. Fourier (Grenoble) 53 (2003) 1883 MR2038782
4 D C Cohen, A I Suciu, On Milnor fibrations of arrangements, J. London Math. Soc. $(2)$ 51 (1995) 105 MR1310725
5 P Deligne, Le groupe fondamental du complément d'une courbe plane n'ayant que des points doubles ordinaires est abélien (d'après W. Fulton), from: "Bourbaki Seminar, Vol. 1979/80", Lecture Notes in Math. 842, Springer (1981) 1 MR636513
6 A Dimca, Singularities and topology of hypersurfaces, Universitext, Springer (1992) MR1194180
7 A Dimca, Sheaves in topology, Universitext, Springer (2004) MR2050072
8 A Dimca, Hyperplane arrangements, $M$–tame polynomials and twisted cohomology, from: "Commutative algebra, singularities and computer algebra (Sinaia, 2002)", NATO Sci. Ser. II Math. Phys. Chem. 115, Kluwer Acad. Publ. (2003) 113 MR2030266
9 A Dimca, A Némethi, Hypersurface complements, Alexander modules and monodromy, from: "Real and complex singularities", Contemp. Math. 354, Amer. Math. Soc. (2004) 19 MR2087802
10 A Dimca, S Papadima, Hypersurface complements, Milnor fibers and higher homotopy groups of arrangments, Ann. of Math. $(2)$ 158 (2003) 473 MR2018927
11 A Dimca, Ş Papadima, Equivariant chain complexes, twisted homology and relative minimality of arrangements, Ann. Sci. École Norm. Sup. $(4)$ 37 (2004) 449 MR2060483
12 M Falk, Homotopy types of line arrangements, Invent. Math. 111 (1993) 139 MR1193601
13 K M Fan, Direct product of free groups as the fundamental group of the complement of a union of lines, Michigan Math. J. 44 (1997) 283 MR1460414
14 W Fulton, On the fundamental group of the complement of a node curve, Ann. of Math. $(2)$ 111 (1980) 407 MR569076
15 A Hattori, Topology of $C^{n}$ minus a finite number of affine hyperplanes in general position, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 22 (1975) 205 MR0379883
16 J A Hillman, Alexander ideals of links, Lecture Notes in Mathematics 895, Springer (1981) MR653808
17 P J Hilton, U Stammbach, A course in homological algebra, Graduate Texts in Mathematics 4, Springer (1971) MR0346025
18 M Jambu, S Papadima, A generalization of fiber-type arrangements and a new deformation method, Topology 37 (1998) 1135 MR1632975
19 T Jiang, S S T Yau, Topological invariance of intersection lattices of arrangements in $\mathbb{C}\mathrm{P}^2$, Bull. Amer. Math. Soc. $($N.S.$)$ 29 (1993) 88 MR1197426
20 T Jiang, S S T Yau, Diffeomorphic types of the complements of arrangements of hyperplanes, Compositio Math. 92 (1994) 133 MR1283226
21 Y Kawahara, The mixed Hodge structure on the fundamental group of a complement of hyperplanes, Topology Appl. 118 (2002) 131 MR1877720
22 A Libgober, Alexander modules of plane algebraic curves, from: "Low-dimensional topology (San Francisco, Calif., 1981)", Contemp. Math. 20, Amer. Math. Soc. (1983) 231 MR718145
23 A Libgober, Alexander invariants of plane algebraic curves, from: "Singularities, Part 2 (Arcata, Calif., 1981)", Proc. Sympos. Pure Math. 40, Amer. Math. Soc. (1983) 135 MR713242
24 A Libgober, Homotopy groups of the complements to singular hypersurfaces. II, Ann. of Math. $(2)$ 139 (1994) 117 MR1259366
25 A Libgober, The topology of complements to hypersurfaces and nonvanishing of a twisted de Rham cohomology, from: "Singularities and complex geometry (Beijing, 1994)", AMS/IP Stud. Adv. Math. 5, Amer. Math. Soc. (1997) 116 MR1468273
26 A Libgober, Eigenvalues for the monodromy of the Milnor fibers of arrangements, from: "Trends in singularities", Trends Math., Birkhäuser (2002) 141 MR1900784
27 J Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies 61, Princeton University Press (1968) MR0239612
28 M Oka, K Sakamoto, Product theorem of the fundamental group of a reducible curve, J. Math. Soc. Japan 30 (1978) 599 MR513072
29 P Orlik, L Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980) 167 MR558866
30 P Orlik, H Terao, Arrangements of hyperplanes, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer (1992) MR1217488
31 P Orlik, H Terao, Arrangements and hypergeometric integrals, MSJ Memoirs 9, Mathematical Society of Japan (2001) MR1814008
32 Ş Papadima, Generalized $\mu$–invariants for links and hyperplane arrangements, Proc. London Math. Soc. $(3)$ 84 (2002) 492 MR1881400
33 S Papadima, A I Suciu, Higher homotopy groups of complements of complex hyperplane arrangements, Adv. Math. 165 (2002) 71 MR1880322
34 R Randell, Lattice-isotopic arrangements are topologically isomorphic, Proc. Amer. Math. Soc. 107 (1989) 555 MR984812
35 R Randell, Homotopy and group cohomology of arrangements, Topology Appl. 78 (1997) 201 MR1454600
36 G Rybnikov, On the fundamental group of the complement of a complex hyperplane arrangement, DIMACS technical report 94-13 (1994) 33 arXiv:math.AG/9805056
37 D Siersma, The vanishing topology of non isolated singularities, from: "New developments in singularity theory (Cambridge, 2000)", NATO Sci. Ser. II Math. Phys. Chem. 21, Kluwer Acad. Publ. (2001) 447 MR1849319
38 J Stallings, A finitely presented group whose 3–dimensional integral homology is not finitely generated, Amer. J. Math. 85 (1963) 541 MR0158917
39 G W Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics 61, Springer (1978) MR516508
40 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