A Degree Doubling Formula for Braid Monodromies and Lefschetz Pencils

@article{Auroux2006ADD,
  title={A Degree Doubling Formula for Braid Monodromies and Lefschetz Pencils},
  author={D. Auroux and L. Katzarkov},
  journal={Pure and Applied Mathematics Quarterly},
  year={2006},
  volume={4},
  pages={237-318}
}
  • D. Auroux, L. Katzarkov
  • Published 2006
  • Mathematics
  • Pure and Applied Mathematics Quarterly
  • Every compact symplectic 4-manifold can be realized as a branched cover of the complex projective plane branched along a symplectic curve with cusp and node singularities; the covering map is induced by a triple of sections of a "very ample" line bundle. In this paper, we give an explicit formula describing the behavior of the braid monodromy invariants of the branch curve upon degree doubling of the linear system (from a very ample bundle $L^k$ to $L^{2k}$). As a consequence, we derive a… CONTINUE READING
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