On the exponents of free and nearly free projective plane curves

Abstract

We show that all the possible pairs of integers occur as exponents for free or nearly free irreducible plane curves and line arrangements, by producing only two types of simple families of examples. The topology of the complements of these curves and line arrangements is also discussed, and many of them are shown not to be \(K(\pi ,1)\) spaces.

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Correspondence to Alexandru Dimca.

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Alexandru Dimca: Partially supported by Institut Universitaire de France.

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Dimca, A., Sticlaru, G. On the exponents of free and nearly free projective plane curves. Rev Mat Complut 30, 259–268 (2017). https://doi.org/10.1007/s13163-017-0228-3

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Keywords

  • Jacobian ideal
  • Tjurina number
  • Free curve
  • Nearly free curve

Mathematics Subject Classification

  • Primary 14H50
  • Secondary 14B05
  • 13D02
  • 32S22