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Combinatorics and topology of line arrangements in the complex projective plane

Author: Enrique Artal-Bartolo
Journal: Proc. Amer. Math. Soc. 121 (1994), 385-390
MSC: Primary 14F45; Secondary 14F25, 32S35, 52B30
MathSciNet review: 1189536
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Abstract: We use some results about Betti numbers of coverings of complements of plane projective curves to discuss the problem of how combinatorics determine the topology of line arrangement, finding a counterexample to a conjecture of Orlik.

References [Enhancements On Off] (What's this?)

  • [A] E. Artal, Les couples de Zariski, J. Algebraic Geom. (to appear).
  • [BPV] W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer-Verlag, Berlin, 1984. MR 749574
  • [E] Hélène Esnault, Fibre de Milnor d’un cône sur une courbe plane singulière, Invent. Math. 68 (1982), no. 3, 477–496 (French). MR 669426,
  • [O] P. Orlik, Introduction to arrangements, Proc. Sympos. Pure Math., vol. 72, Amer. Math. Soc., Providence, RI, 1989.
  • [Z1] O. Zariski, On the linear connection index of the algebraic surfaces, Proc. Nat. Acad. Sci. U.S.A. 15 (1929), 494-501.
  • [Z2] Oscar Zariski, On the irregularity of cyclic multiple planes, Ann. of Math. (2) 32 (1931), no. 3, 485–511. MR 1503012,

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Keywords: Singularity, Milnor fiber, combinatorics, Betti numbers, arrangements
Article copyright: © Copyright 1994 American Mathematical Society