Effective invariants of braid monodromy

Artal Bartolo, Enrique; Carmona Ruber, Jorge; Cogolludo Agustín, José

doi:10.1090/S0002-9947-06-03881-5

Effective invariants of braid monodromy
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by Enrique Artal Bartolo, Jorge Carmona Ruber and José Ignacio Cogolludo Agustín PDF

Trans. Amer. Math. Soc. 359 (2007), 165-183 Request permission

Abstract:

In this paper we construct new invariants of algebraic curves based on (not necessarily generic) braid monodromies. Such invariants are effective in the sense that their computation allows for the study of Zariski pairs of plane curves. Moreover, the Zariski pairs found in this work correspond to curves having conjugate equations in a number field, and hence are not distinguishable by means of computing algebraic coverings. We prove that the embeddings of the curves in the plane are not homeomorphic. We also apply these results to the classification problem of elliptic surfaces.

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